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# History of Moldova ## Part of Greater Romania {#part_of_greater_romania} After 1918 Bessarabia was under Romanian jurisdiction for the next 22 years. This fact was recognized in the 1920 Treaty of Paris which, however, has never come into force since it was not ratified by Japan. The newly communist Russia did not ...
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# History of Moldova ## World War II and Soviet era {#world_war_ii_and_soviet_era} After the establishment of the Soviet Union in December 1922, the Soviet government moved in 1924 to establish the Moldavian Autonomous Oblast on the lands to the east of the Dniester River in the Ukrainian SSR. The capital of the obla...
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# History of Moldova ## Independent Republic of Moldova {#independent_republic_of_moldova} ### Perestroika and Glasnost {#perestroika_and_glasnost} In the climate of Mikhail Gorbachev\'s perestroika and glasnost, national sentiment escalated in the Moldavian SSR in 1988. In 1989, the Popular Front of Moldova was for...
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# History of Moldova ## Independent Republic of Moldova {#independent_republic_of_moldova} ### Early years of independence (1991--2001) {#early_years_of_independence_19912001} On 8 December 1991, Mircea Snegur, an ex-communist reformer, ran an unopposed election for the presidency. On March 2, 1992, the country achie...
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# History of Moldova ## Independent Republic of Moldova {#independent_republic_of_moldova} ### Dominance of the Communists (2001--2009) {#dominance_of_the_communists_20012009} Only 3 of the 31 political parties won more than the 6% of the popular vote required to win seats in parliament in the February 25, 2001 elect...
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# History of Moldova ## Independent Republic of Moldova {#independent_republic_of_moldova} ### Liberal Democrat and Socialist administrations {#liberal_democrat_and_socialist_administrations} An attempt by the new ruling coalition to amend the constitution of Moldova via a referendum in 2010 in order to enable presid...
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# History of Moldova ## Independent Republic of Moldova {#independent_republic_of_moldova} ### Presidency of Maia Sandu since 2020 {#presidency_of_maia_sandu_since_2020} In the November 2020 presidential election, the pro-European opposition candidate Maia Sandu was elected as the new president of the republic, becom...
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# History of Moldova ## Independent Republic of Moldova {#independent_republic_of_moldova} ### Presidency of Maia Sandu since 2020 {#presidency_of_maia_sandu_since_2020} #### Russia-related events since the invasion of neighbouring Ukraine {#russia_related_events_since_the_invasion_of_neighbouring_ukraine} In Februar...
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# Geography of Moldova Located in Eastern Europe, Moldova is bordered on the west and southwest by Romania and on the north, south, and east by Ukraine. Most of its territory lies in Bessarabia region, between the area\'s two main rivers, the Nistru and the Prut. The Nistru forms a small part of Moldova\'s border with...
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# Geography of Moldova ## Climate Moldova\'s proximity to the Black Sea gives it a mild and sunny climate. Moldova\'s climate is moderately continental: the summers are warm and long, with temperatures averaging about 20 °C, and the winters are relatively mild and dry, with January temperatures averaging −2 °C...
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# Geography of Moldova ## Topography Most of Moldova\'s territory is a moderate hilly plateau cut deeply by many streams and rivers. Geologically, Moldova lies primarily on the deep sedimentary rock that gives way to harder crystalline outcroppings only in the north. Moldova\'s hills are part of the larger Moldavian ...
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# Geography of Moldova ## Natural habitat {#natural_habitat} Moldova\'s natural habitat is characterized by forest steppes, a temperate-climate habitat type composed of grassland interspersed with areas of woodland or forest. A belt of forest steppes cross Eurasia from eastern Europe to Eastern Siberia, forming a tra...
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# Politics of Moldova The **politics of Moldova** take place in a framework of a parliamentary representative democratic republic, wherein the prime minister is the head of the Government of Moldova, and a multi-party system. The President of Moldova has no important powers. The government exercises executive power wh...
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# Politics of Moldova ## Issues ### Ethnic identity and unification with Romania {#ethnic_identity_and_unification_with_romania} The underlying issue in the Republic of Moldova revolves around ethnicity and whether the country should re-unite with Romania, with which it shares a common ethnicity, language, culture a...
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# Politics of Moldova ## Issues ### Other issues {#other_issues} There is disagreement as to whether elections and politics in Moldova are carried out in a free and democratic climate on the part of certain organizations. The United States Senate has held committee hearings on irregularities that marred elections in ...
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# Telecommunications in Moldova **Telecommunications in Moldova** are maintained at a relatively high performance level. Because Moldova is a small country, telecommunications companies managed to achieve good coverage in both wired and wireless communications infrastructure. Landline is available in most settlements,...
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# Telecommunications in Moldova ## Mobile telephony {#mobile_telephony} The mobile telephone market of Moldova is divided between two GSM carriers - Orange Moldova and Moldcell, and two CDMA carriers - Unité and Interdnestrcom. Orange Moldova launched its network in October 1998 under the brand of Voxtel and was the ...
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# Telecommunications in Moldova ## Internet Moldova has one of the best wired Internet connections in the world as well as one of the cheapest in terms of \$ per Mbit. The overall infrastructure is well developed which allows many users to experience good quality services throughout the country. However, despite high...
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# Telecommunications in Moldova ## Television Television industry in Moldova began in 1956 with the construction of the country\'s first dedicated television tower in Chişinău which took a little over a year to complete, the finished tower was 196 meters tall and could broadcast within a 60 km radius. The first telev...
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# History of Monaco The early **history of Monaco** is primarily concerned with the protective and strategic value of the Rock of Monaco, the area\'s chief geological landmark, which served first as a shelter for ancient peoples and later as a fortress. Part of Liguria\'s history since the fall of the Roman Empire, fr...
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# History of Monaco ## Dark ages to the Genoese {#dark_ages_to_the_genoese} Monaco remained under Roman control until the collapse of the Western Roman Empire in 476. The city was then under the domain of Odoacer until his fall at the hands of the Ostrogoths in the late 5th century. Monaco was recaptured by the Roman...
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# History of Monaco ## Middle Ages: Rise of the Grimaldis {#middle_ages_rise_of_the_grimaldis} The Grimaldis, descended from Otto Canella and taking their name from his son Grimaldo, were an ancient and prominent Guelphic Genoese family. Members of this family, in the course of the civil strife in Genoa between the G...
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# History of Monaco ## 20th century {#th_century} The Prince of Monaco was an absolute ruler until the Monegasque Revolution of 1910 forced him to proclaim a constitution in 1911. In July 1918, a treaty was signed providing for limited French protection over Monaco. The treaty, written into the Treaty of Versailles,...
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# Demographics of Monaco / sq. km. `| growth             = 2.25% (2012–13)`\ `| birth              = 13.1 (2015)`\ `| death              = 10.4 (2015)`\ `| life               = 84.7 (2011–13)`\ `| life_male          = `\ `| life_female        = `\ `| infant_mortality   =`\ `| fertility          = 1.52 (2018)` `| age...
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# Demographics of Monaco ## Demographic statistics {#demographic_statistics} ### Structure of the population {#structure_of_the_population} Age Group Male Female Total \% ----------- -------- -------- -------- --------- Total 15 076 15 914 31 109 100 0--4 577 557 1 134 ...
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# Politics of Monaco The **politics of Monaco** take place within the framework of a semi-constitutional monarchy, with the Prince of Monaco as head of state, with some powers devolved to several advisory and legislative bodies. ## Constitution Historically, the princes of the ruling House of Grimaldi were autocrats...
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# Politics of Monaco ## International organization participation {#international_organization_participation} ACCT, ECE, International Atomic Energy Agency, International Civil Aviation Organization, ICRM, IFRCS, IHO, IMO, Inmarsat, Intelsat, Interpol, International Olympic Committee, ITU, OPCW, OSCE, United Nations, ...
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# Economy of Monaco The **economy of Monaco** is reliant on tourism and banking. Monaco, situated on the French coast of the Mediterranean Sea, is a popular resort, attracting tourists to its casino and pleasant climate. The Principality has successfully sought to diversify into services and small, high-value-added, ...
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# Economy of Monaco ## Tax haven {#tax_haven} Monaco levies no income tax on individuals. The absence of a personal income tax in the principality has attracted to it a considerable number of wealthy \"tax refugee\" residents from European countries who derive the majority of their income from activity outside Monaco...
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# Transport in Monaco **Transport in Monaco** is facilitated with road, air (helicopter), rail, and water networks. Rail transport is operated by SNCF with only Monaco Monte Carlo station seeing passenger service and the total length of the line inside the Principality is 1.7 km. Monaco has five bus routes operated by...
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# Transport in Monaco ## Air transport {#air_transport} ### Airports There is no airport in the Principality of Monaco. The closest airport is Cote d\'Azur Airport in Nice, France, which is connected to Monaco by the Express 110 bus. Alternatively passengers can take Nice tramway lines 2 and 3 to downtown Nice and t...
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# Public Services (Monaco) *Pandoc failed*: ``` Error at (line 102, column 1): unexpected '{' {{Ranks and Insignia of Non NATO Armed Forces/OF/Blank}} ^ ``
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# Geography of Mongolia Mongolia is a landlocked country in East Asia, located between China and Russia. The terrain is one of mountains and rolling plateaus, with a high degree of relief. The total land area of Mongolia is 1,564,116 square kilometres. Overall, the land slopes from the high Altai Mountains of the west...
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# Geography of Mongolia ## Climate ### Overview Mongolia has a high elevation, with a cold and dry climate. It has an extreme continental climate with long, very cold winters and short summers, during which most precipitation falls. The country averages 257 cloudless days a year, and it is usually at the center of a...
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# Telecommunications in Mongolia **Telecommunications in Mongolia** face unique challenges. As the least densely populated country in the world, with a significant portion of the population living a nomadic lifestyle, it has been difficult for many traditional information and communication technology (ICT) companies t...
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# Telecommunications in Mongolia ## Television Mongolian TV Broadcasting started on 27 September 1967 with the start of Mongolian National Television. - Television sets: 118,000 (1997) ### Television providers {#television_providers} Stations/Channels - Mongolian National Broadcaster, the official, state-fund...
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# Transport in Mongolia The **transportation system** in Mongolia consists of a network of railways, roads, waterways, and airports. ## Railways The Trans-Mongolian Railway connects the Trans-Siberian Railway from Ulan Ude in Russia to Erenhot and Beijing in China through the capital Ulaanbaatar. The Mongolian secti...
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# Transport in Mongolia ## Air transport {#air_transport} `{{See also|MIAT Mongolian Airlines}}`{=mediawiki} MIAT Mongolian Airlines is the country\'s flag carrier and first airline, operating since 1956. It conducted scheduled domestic flights in the communist era with its hub at Buyant-Ukhaa International Airport (...
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# Demographics of Montserrat This is demography of the population of Montserrat including population density, ethnicity, education level, health of the populace, economic status, religious affiliations and other aspects of the population. ## Population Montserrat had a population of 7,119 in 1842. In 1995, the Souf...
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# Demographics of Montserrat ## Vital statistics {#vital_statistics} Average population (x 1000) Live births Deaths Natural change Crude birth rate (per 1000) Crude death rate (per 1000) Natural change (per 1000) TFR ------ ----------------------------- ------------- -------- ----------------...
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# Politics of Montserrat **Politics of Montserrat** takes place in a framework of a parliamentary representative democratic dependency, whereby the Premier is the head of government, and of a multi-party system. **Montserrat** is an internally self-governing overseas territory of the United Kingdom. The United Nations...
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# Economy of Montserrat The **economy of Montserrat** is an economical system which was severely disrupted by volcanic activity which began in July 1995. Prior to this date, the small island country of 12,000 had an export economy based on agriculture, clothing, electronic parts and plants, with a per capita gross nat...
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# Telecommunications in Montserrat Montserrat possesses a number of **telecommunications systems**, including mobile and main line telephone, radio and television. The country code for Montserrat in the Domain Name System of the Internet is \".ms\". Telephony uses the area code 664. According to a July 2016 estimate ...
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# Transport in Montserrat **Railways:** 0 km **Highways:**\ *total:* 269 km\ *paved:* 203 km\ *unpaved:* 66 km (1995) **Waterways:** none **Ports and harbours:** Plymouth (abandoned), Little Bay (anchorages and ferry landing), Carr\'s Bay **Merchant marine:** none (2002 est.) **Airports:** One, Gerald\'s Airport,...
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# Geography of Morocco Morocco is the northwesternmost country which spans from the Mediterranean Sea and Atlantic Ocean on the north and the west respectively, into large mountainous areas in the interior, to the Sahara desert in the far south. Morocco is a Northern African country, located in the extreme northwest o...
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# Geography of Morocco ## Climate Morocco\'s climate can be divided into two parts: The northwest and the southeast. In the southeast, the climate is arid and poorly populated. The northwest has a mild climate, and 95% of the Moroccan population lives in these regions. The largely populated areas of the northwest of...
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# Geography of Morocco ## Extreme points {#extreme_points} This is a list of the extreme points of Morocco, the points that are farther north, east or west than any other location. - Northernmost point -- Pointe Leona, Tanger-Tetouan-Al Hoceima region - Easternmost point -- unnamed point on the border with Alger...
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# Demographics of Morocco Demographic features of the population of Morocco include population density, ethnicity, religious affiliations and other aspects of the population. All figures are from the Haut-Commissariat au Plan of Morocco or the United Nations Demographic Yearbooks, unless otherwise indicated. The popu...
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# Demographics of Morocco ## Population size and structure {#population_size_and_structure} ### Main populated areas {#main_populated_areas} Most Moroccans live west and north of the Atlas Mountains, a range that insulates the country from the Sahara Desert. Casablanca is the largest city and the centre of business ...
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# Demographics of Morocco ## Vital statistics {#vital_statistics} Average population Live births Deaths Natural change Crude birth rate (per 1,000) Crude death rate (per 1,000) Natural change (per 1,000) Fertility rates ------ -------------------- ------------------- --------- --------...
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# Demographics of Morocco ## Ethnic groups {#ethnic_groups} `{{Pie chart|caption=Ethnic groups in Morocco (2012)<ref name="OxfordBusinessGroup" />|label1=[[Arabs]]|label2=[[Berbers]]|label3=[[Sahrawis]]|value1=67|value2=31|value3=2|color1=DarkGreen|color2=Yellow|color3=Purple|color4=Pink|color5=Cyan}}`{=mediawiki}Mor...
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# Demographics of Morocco ## Languages Arabic and Berber are the official languages of Morocco. The majority spoken language in Morocco is Arabic which is spoken by 92.7% of the population and includes the dialects of Moroccan Arabic (Hilalian dialects), spoken by 91.9%, and Hassaniya Arabic, spoken by 0.8%. Berber l...
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# Politics of Morocco **Politics of Morocco** take place in a framework of an official parliamentary semi-constitutional islamic monarchy, whereby the prime minister of Morocco is the head of government, and of a multi-party system. Executive power is exercised by the government. Legislative power is vested in both th...
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# Politics of Morocco ## Administrative divisions {#administrative_divisions} Since 2015 Morocco officially administers 12 regions: Béni Mellal-Khénifra, Casablanca-Settat, Dakhla-Oued Ed-Dahab, Drâa-Tafilalet, Fès-Meknès, Guelmim-Oued Noun, Laâyoune-Sakia El Hamra, Marrakech-Safi, Oriental, Rabat-Salé-Kénitra, Souss...
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# Transport in Morocco There are around 56986 km of roads (national, regional and provincial) in Morocco. In addition to 1808 km of highways (August 2016). The Tangier--Casablanca high-speed rail link marks the first stage of the ONCF\'s high-speed rail master plan, pursuant to which over 1500 km of new railway lines...
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# Transport in Morocco ## Roads As of 2006 there were around 57625 kilometres of roads (national, regional and provincial) in Morocco, and an additional 1808 kilometers of highways (August 2016). Principal national roads: - National Route 1 (Morocco) - National Route 2 (Morocco) - National Route 3 (Morocco) -...
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# History of Mozambique Mozambique was a Portuguese colony, overseas province and later a member state of Portugal. It gained independence from Portugal in 1975. ## Pre-colonial history {#pre_colonial_history} ### Prehistoric Mozambique {#prehistoric_mozambique} In 2007 Julio Mercader, of the University of Calgary,...
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# History of Mozambique ## Portuguese Mozambique (1498--1975) {#portuguese_mozambique_14981975} From about 1500, Portuguese trading posts and forts displaced the Arabic commercial and military hegemony, becoming regular ports of call on the new European sea route to the east. The voyage of Vasco da Gama around the C...
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# History of Mozambique ## Independence (1975) {#independence_1975} After 10 years of sporadic warfare and Portugal\'s return to democracy through a leftist military coup in Lisbon, which replaced Portugal\'s Estado Novo regime with a military junta (the Carnation Revolution of April 1974), FRELIMO took control of th...
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# History of Mozambique ## Democratic era (1994--present) {#democratic_era_1994present} Mozambique held elections in 1994, which were accepted by most parties as free and fair while still contested by many nationals and observers alike. FRELIMO won, under Joaquim Chissano, while RENAMO, led by Afonso Dhlakama, ran as...
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# Geography of Mozambique upright=1.4\|thumb\|Map of Mozambique\'s population centres thumb\|upright=1.3\|Mozambique\'s topography thumb\|upright=1.3\|A view of the Zambezi river delta from space. The **geography of Mozambique** consists mostly of coastal lowlands with uplands in its centre and high plateaus in the n...
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# Geography of Mozambique ## Physical features {#physical_features} ### Somali Plate {#somali_plate} Geologists have divided the Phanerozoic era of Mozambique\'s geology into the Karoo and post-Karoo era. This terminology is mostly used pertaining to studies of the structural and stratigraphic composition of rocks in...
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# Geography of Mozambique ## Facts Area: :\*Total: 801,590 km2 :\*\**country rank in the world:* 35th :\* Land: 786,380 km² :\*Water: 13,000 km² Area comparative :\* Australia comparative: approximately the size of New South Wales :\* Canada comparative: slightly less than twice the size of Newfoundland and La...
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# Demographics of Mozambique The **demographics of Mozambique** describes the condition and overview of Mozambique\'s peoples. Demographic topics include basic education, health, and population statistics as well as identified racial and religious affiliations. ## Population According to the 2022 revision of the wor...
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# Demographics of Mozambique ## Vital statistics {#vital_statistics} Registration of vital events is in Mozambique not complete. The website Our World in Data prepared the following estimates based on statistics from the Population Department of the United Nations. Mid-year population (thousands) Live bir...
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# Demographics of Mozambique ## Vital statistics {#vital_statistics} ### Life expectancy {#life_expectancy} +------------+---------------------+ | Period | Life expectancy in\ | | | Years | +============+=====================+ | 1950--1955 | 31.29 | +------------+-----------...
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# Demographics of Mozambique ## Languages Portuguese is the official and most widely spoken language of the nation, but in 2017 only 47.4% of Mozambique\'s population speak Portuguese as either their first or second language, and only 16.6% speak Portuguese as their first language. Arabs, Chinese, and Indians speak t...
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# Politics of Mozambique **Politics in Mozambique** takes place in a framework of a semi-presidential representative democratic republic, whereby the President of Mozambique is head of state and head of government in a multi-party system. Executive power is exercised by the government. Legislative power is vested in b...
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# Politics of Mozambique ## Legislative branch {#legislative_branch} The Assembly of the Republic (*Assembleia da República*) has 250 members, elected for a five-year term by proportional representation. ## Political parties and elections {#political_parties_and_elections} In 1994 the country held its first democra...
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# Politics of Mozambique ## Administrative divisions {#administrative_divisions} Mozambique is divided in 10 provinces (provincias, singular - provincia); Cabo Delgado, Gaza, Inhambane, Manica, Maputo, Nampula, Niassa, Sofala, Tete, Zambezia ## International organisation participation {#international_organisation_pa...
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# Transport in Mozambique Modes of transport in Mozambique include rail, road, water, and air. There are rail links serving principal cities and connecting the country with Malawi, Zimbabwe and South Africa. There are over 30,000 km of roads, but much of the network is unpaved. On the Indian Ocean coast are several l...
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# Transport in Mozambique ## Roads and highways {#roads_and_highways} Mozambique\'s inter-city roads are classified as a national or primary road (*estrada nacional* or *estrada primária*), or as regional -- secondary or tertiary -- roads (*estradas secundárias* and *estradas terciáreas*). National roads are given th...
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# Mozambique Defence Armed Forces fleet admiral}} `{{Use dmy dates|date=July 2021}}`{=mediawiki} `{{Infobox national military | name = Mozambique Defence Armed Forces | native_name = {{native name|pt|Forças Armadas de Defesa de Moçambique}} | image2 = Flag of the Mozambique Defence Armed Forces.svg | caption2 = Flag o...
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# Mozambique Defence Armed Forces ## History Coelho et al write: \"Independence in June 1975 was preceded by a nine-month transition period in which Frelimo took control of a transitional cabinet where ..it held six of the nine ministries.\" The previous Forças Populares de Libertação de Moçambique (FPLM), the armed ...
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# Mozambique Defence Armed Forces ## Land Forces {#land_forces} The Mozambican Army was formed in 1976 from three conventional battalions, two of which were trained in Tanzania and a third of which was trained in Zambia. Army officer candidates were initially trained in Maputo by Chinese military instructors. In Marc...
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# Mozambique Defence Armed Forces ## Air Force {#air_force} ## Navy There are about 200 personnel in the navy. In September 2004 it was reported that the South African Navy was to donate two of its Namacurra class harbour patrol boat to the Mozambique Navy. The boats were refitted by the naval dockyard at Simon\'s T...
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# Master shot A **master shot** (or short **master**) is a film recording of an entire dramatized scene, start to finish, from a camera angle that keeps all the players in view. It is often a long shot and can sometimes perform a double function as an establishing shot. Usually, the master shot is the first shot check...
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# Medium shot In a movie a **medium shot**, **mid shot** (**MS**), or **waist shot** is a camera angle shot from a medium distance. ## Use Medium shots are favored in sequences where dialogues or a small group of people are acting, as they give the viewer a partial view of the background, such as when the shot is \'...
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# Index of articles related to motion pictures The film industry is built upon many technologies and techniques, drawing upon photography, stagecraft, music, and many other disciplines. Following is an index of specific terminology applicable thereto
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# Mountain range Mountain range (options)}} thumb\|upright=1.5\|The Namcha Barwa Himal, east part of the Himalayas as seen from space by Apollo 9 A **mountain range** or **hill range** is a series of mountains or hills arranged in a line and connected by high ground. A **mountain system** or **mountain belt** is a g...
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# Magnoliales The **Magnoliales** are an order of flowering plants. Well-known members of Magnoliales include: magnolias, tulip trees, custard apples, American pawpaw, cherimoyas, ylang-ylang, soursop fruit, and nutmeg. ## Classification The Magnoliales include six families: - Annonaceae (custard apple family, ov...
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# March MAR}} `{{pp-move}}`{=mediawiki} `{{Calendar}}`{=mediawiki} **March** is the third month of the year in both the Julian and Gregorian calendars. Its length is 31 days. In the Northern Hemisphere, the meteorological beginning of spring occurs on the first day of March. The March equinox on the 20 or 21 marks th...
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# March ## Observances *This list does not necessarily imply either official status or general observance.* ### Month-long {#month_long} - In Catholic tradition, March is the Month of Saint Joseph. - Endometriosis Awareness Month (International observance) - National Nutrition Month (Canada) - Season for No...
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# March ## Observances ### Fixed - March 1 - Baba Marta (Bulgaria), - Beer Day (Iceland) - Commemoration of Mustafa Barzani\'s Death (Iraqi Kurdistan) - Heroes\' Day (Paraguay) - Independence Day (Bosnia and Herzegovina) - Mărțișor (Romania and Moldavia) - National Pig Day ...
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# March 28
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# May 3
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# May 4
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# May 5
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# Matteo Carcassi **Matteo Carcassi** (8 April 1792 -- 16 January 1853) was an Italian guitarist and composer. ## Life Carcassi was born in Florence, Italy, and first studied the piano, but learned guitar when still a child. He quickly gained a reputation as a virtuoso concert guitarist. He moved to Germany in 1810...
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# Microelectronics **Microelectronics** is a subfield of electronics. As the name suggests, microelectronics relates to the study and manufacture (or microfabrication) of very small electronic designs and components. Usually, but not always, this means micrometre-scale or smaller. These devices are typically made from...
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# Mondino **Mondino** is an Italian surname
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# Multivariate statistics **Multivariate statistics** is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., *multivariate random variables*. Multivariate statistics concerns understanding the different aims and background of each of the different...
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# Multivariate statistics ## Multivariate analysis {#multivariate_analysis} ### Types of analysis {#types_of_analysis} Many different models are used in MVA, each with its own type of analysis: 1. Multivariate analysis of variance (MANOVA) extends the analysis of variance to cover cases where there is more than one...
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# Multivariate statistics ## History C.R. Rao made significant contributions to multivariate statistical theory throughout his career, particularly in the mid-20th century. One of his key works is the book titled \"Advanced Statistical Methods in Biometric Research,\" published in 1952. This work laid the foundation ...
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# Group (mathematics) In mathematics, a **group** is a set with an operation that combines any two elements of the set to produce a third element within the same set and the following conditions must hold: the operation is associative, it has an identity element, and every element of the set has an inverse element. Fo...
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# Group (mathematics) ## Definition and illustration {#definition_and_illustration} ### First example: the integers {#first_example_the_integers} One of the more familiar groups is the set of integers $\Z = \{\ldots,-4,-3,-2,-1,0,1,2,3,4,\ldots\}$ together with addition. For any two integers $a$ and `{{tmath|1= b }}...
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# Group (mathematics) ## Definition and illustration {#definition_and_illustration} ### Notation and terminology {#notation_and_terminology} Formally, a group is an ordered pair of a set and a binary operation on this set that satisfies the group axioms. The set is called the *underlying set* of the group, and the op...
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# Group (mathematics) ## Definition and illustration {#definition_and_illustration} ### Second example: a symmetry group {#second_example_a_symmetry_group} Two figures in the plane are congruent if one can be changed into the other using a combination of rotations, reflections, and translations. Any figure is congrue...
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# Group (mathematics) ## History The modern concept of an abstract group developed out of several fields of mathematics. The original motivation for group theory was the quest for solutions of polynomial equations of degree higher than 4. The 19th-century French mathematician Évariste Galois, extending prior work of ...
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# Group (mathematics) ## Elementary consequences of the group axioms {#elementary_consequences_of_the_group_axioms} Basic facts about all groups that can be obtained directly from the group axioms are commonly subsumed under *elementary group theory*. For example, repeated applications of the associativity axiom show...
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