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[ "For example , if the angle between the road and the uphill direction , projected onto the horizontal plane , is 60 ° , then the steepest slope along the road will be 20 % , which is 40 % times the cosine of 60 ° .", "For example , if the angle between the road and the uphill direction , projected onto the horizo...
[ "At each point in the room , the gradient of T at that point will show the direction the temperature rises most quickly .", "Then , at each point in the room , the gradient at that point will show the direction in which the temperature rises most quickly ." ]
[ "The gradient of H at a point is a vector pointing in the direction of the steepest slope or grade at that point .", "The gradient of at a point is a vector pointing in the direction of the steepest slope or grade at that point ." ]
[ "( We will assume that the temperature does not change over time . )", "We will assume that the temperature does not change in time ." ]
[ "Suppose that the steepest slope on a hill is 40 % .", "Consider again the example with the hill and suppose that the steepest slope on the hill is 40 % ." ]
[ "If , instead , the road goes around the hill at an angle , then it will have a shallower slope .", "If instead , the road goes around the hill at an angle with the uphill direction ( the gradient vector ) , then it will have a shallower slope ." ]
[ "Consider a room in which the temperature is given by a scalar field , T , so at each point ( x , y , z ) the temperature is T ( x , y , z ) .", "Consider a room in which the temperature is given by a scalar field , so at each point the temperature is ." ]
[ "Consider a surface whose height above sea level at a point ( x , y ) is H ( x , y ) .", "Consider a hill whose height above sea level at a point is ." ]
[ "The brush-tailed rock-wallaby or small-eared rock-wallaby ( Petrogale penicillata ) is a kind of wallaby , one of several rock-wallabies in the genus Petrogale .", "The brush-tailed rock-wallaby or small-eared rock-wallaby ( Petrogale penicillata ) is a kind of wallaby ." ]
[ "As part of the acclimatisation movement of the late 1800s , governor Grey introduced this and four other species of wallabies ( including the rare parma wallaby ) to islands in Hauraki Gulf , near Auckland , New Zealand , where they became well-established .", "In the late 1800s , governor Grey introduced this a...
[ "Another thirty-three rock-wallabies were captured on Kawau during the 2000s , and returned to Australia , before eradication began .", "Another 33 rock-wallabies were captured on Kawau during the 2000s , and returned to Australia ." ]
[ "Populations have declined seriously in the south and west of its range , but it remains locally common in northern New South Wales and southern Queensland .", "It remains locally common in northern New South Wales and southern Queensland ." ]
[ "Rock-wallabies were removed from Rangitoto and Motutapu Islands during the 1990s , and eradication is now underway on Kawau .", "Rock-wallabies were removed from Rangitoto and Motutapu Islands during the 1990s ." ]
[ "In modern times , these populations have come to be viewed as exotic pests , with severe impacts on the indigenous flora and fauna .", "In modern times , the wallabies have come to be viewed as exotic pests ." ]
[ "Due to an escape of a pair in 1916 , a small breeding population of the brush-tailed rock-wallabies also exists on the island of Oahu in Hawaii .", "Two wallabies escaped in 1916 on the island of Oahu in Hawaii ." ]
[ "The spectacled caiman ( Caiman crocodilus ) , also known as the white caiman or common caiman , is a crocodilian reptile found in much of Central and South America .", "The spectacled caiman ( Caiman crocodilus ) , or the common caiman , is a medium sized crocodilian species that lives in the wetland areas of So...
[ "Caimans eat a variety of invertebrates such as insects , crustaceans , and mollusks .", "Spectacled caimans have been known to eat insects , crustaceans , and mollusks ." ]
[ "The species ' common name comes from a bony ridge between the eyes , which gives the appearance of a pair of spectacles .", "The spectacled caiman gets its name from the bony ridge between its eyes , looking like a pair of eyeglasses ." ]
[ "They were promoted to the Primera División de Costa Rica , making their debut in the top flight on 21 August 1949 .", "It became a part of the top league , Primera División de Costa Rica on August 21 , 1949 ." ]
[ "The name is Irish for `` ourselves '' or `` we ourselves '' , although it is frequently mistranslated as `` ourselves alone '' .", "The name is Irish for `` ourselves '' or `` we ourselves '' , although it is frequently wrongly translated as `` ourselves alone '' ." ]
[ "Originating in the Sinn Féin organization founded in 1905 by Arthur Griffith , it took its current form in 1970 after a split within the party ( the other party is Workers ' Party of Ireland ) , and has been associated with the Provisional IRA .", "Beginning with the Sinn Féin organization set up in 1905 by Arth...
[ "The opposing , anti-abstentionist party became known as `` Official Sinn Féin '' .", "Sinn Féin is a political party in Ireland ." ]
[ "Around the same time , Gerry Adams began writing for Republican News , calling for Sinn Féin to become more involved politically .", "The leader of Sinn Féin is Gerry Adams ." ]
[ "In the system of ranked Shinto shrines , Watatsu was listed among the third class of nationally significant shrines or Kokuhei Shōsha ( 国幣小社 ? )", "In the modern system of ranked Shinto Shrines , Watatsu was listed among the 3rd class of nationally significant shrines or Kokuhei Shōsha ( 国幣小社 ? )" ]
[ "is a Japanese Shinto shrine in Sado , Niigata , an island in the Sea of Japan .", "is a Japanese Shinto shrine at Sado , Niigata , which is an island in the Sea of Japan ." ]
[ "Each year in late-April , horseback archery ( yabusame ) takes place at the branch shrine in the town of Hamochi .", "Each year in late-April , horseback archery ( yabusame ) takes place at the branch Hachimangū of Watatsu Shrine in the town of Hamochi ." ]
[ "They can be made from flour , old bread , potatoes , semolina , etc. .", "They can be made from flour , potatoes , old bread , semolina , etc. ." ]
[ "Klöße are also large dumplings , steamed or boiled in hot water , made of dough from grated raw or mashed potatoes , eggs and flour .", "Klöße are large dumplings , steamed or boiled in hot water , made of dough from grated raw or mashed potatoes , eggs and flour ." ]
[ "Königsberger Klopse are not dumplings ; they are made from ground meat and are related to Frikadeller .", "Königsberger Klopse are not dumplings , they are made from ground meat and are related to Frikadeller ." ]
[ "Topfenknödel are made with quark cheese ( Topfen ) , ( Hungarian túrógombóc ) , traditionally topped with cinnamon sugar and served with apple sauce or with streusel .", "Topfenknödel are made with quark cheese ( Topfen ) and are traditionally topped with cinnamon sugar and served with apple sauce or with streus...
[ "In some regions of the United States , klub is used to refer specifically to potato dumplings .", "In some parts of the United States , klub is used to mean potato dumplings ." ]
[ "They are typical components of the Central European cuisine , including Austrian , Croatian , Czech , German , Hungarian , Serbian , Slovenian and Ukrainian and come in many different forms .", "They are normal parts of Austrian , German , Hungarian and Czech cuisine ." ]
[ "Knödel ( singular : der Knödel ) , or Klöße ( singular : der Kloß ) , are large round poached or boiled potato or bread dumplings , made without yeast .", "Knödel or Klöße are large round poached or boiled potato or bread dumplings , made without yeast ." ]
[ "In most versions , they are used as a side dish for meat , like roasted meat or stews .", "In most types , they are used as a side dish for meat ." ]
[ "In Austria and Hungary , large sweet dumplings or plum dumplings called Zwetschkenknödel or Gombotzen are made with flour & potato batter , by wrapping the potato dough around whole plums or apricots , boiled and rolled in hot buttered caramelized bread crumbs ( streusel ) .", "Gombotzen are made with flour & po...
[ "Similar semolina crack dumplings are made with semolina , egg and milk , called Grießklößchen ( Austrian Grießnockerl , Hungarian grízgaluska ) Bread dumplings ( Semmelknödel ) are made with dried white bread , milk and egg yolks ( are sometimes shaped like a loaf of bread , and boiled in a napkin , in which case ...
[ "The club was founded in 1919 as Kapfenberger SC .", "The club was founded in 1919 ." ]
[ "Kapfenberger SV is an Austrian association football club from Kapfenberg .", "The Kapfenberger SV ( official Kapfenberger Sportvereinigung Superfund ) is a football club from Kapfenberg , Styria ." ]
[ "The 2004-05 NHL season was the National Hockey League 's 88th season of operation .", "The 2004-05 NHL season would have been the 88th regular season of the National Hockey League ( NHL ) ." ]
[ "The loss of the 2004-05 season 's games made the NHL the first North American professional sports league to lose an entire season of games because of a labor dispute .", "The loss of the 2004-05 season made the NHL the first North American professional sports league to cancel an entire season because of a labor ...
[ "It was the first time since 1919 when a Spanish flu pandemic canceled the playoffs that the Stanley Cup was not awarded .", "It was also the first time since 1919 that the Stanley Cup was not awarded ." ]
[ "The entire 1,230-game schedule , that was to begin in October , was officially canceled on February 16 , 2005 due to an unresolved lockout that began on September 16 , 2004 .", "The season was canceled on February 16 , 2005 because of an unfinished lockout that began on September 16 , 2004 ." ]
[ "The first manned lunar landing occurred on July 20 , 1969 with the Apollo 11 LM Eagle .", "Finally the fist manned lunar landing occurred on July 20 , 1969 with Apollo 11 LM Eagle ." ]
[ "The Apollo Lunar Module ( LM ) , also ( and originally ) known as the Lunar Excursion Module ( LEM ) , was the lander portion of the Apollo spacecraft built for the US Apollo program by Grumman to carry a crew of two from lunar orbit to the surface and back .", "It was built for the US Apollo program to carry a ...
[ "In April 1970 , the Apollo 13 Lunar Module Aquarius played an unexpected role in saving the lives of the three astronauts after an oxygen tank in the Service Module ruptured , disabling the CSM .", "The Apollo 13 Lunar module , it was called `` aquarius '' , played an unexpected role in saving the lives of the t...
[ "A second unmanned test flight of LM-2 was originally planned , but canceled as unnecessary .", "This was the unmanned lower part of the LM ." ]
[ "When ready to leave the Moon , the LM would separate the descent stage and fire the ascent engine to climb back into orbit , using the descent stage as a launch platform .", "After the two men finished their stay on the surface , the descent stage would serve as the launching base for the ascent engine 's firing...
[ "He currently holds the all-time record for FIFA World Cup goals for the Netherlands with 7 .", "He currently holds the all time record for FIFA World Cup goals for the Netherlands with 7 ." ]
[ "John Nicholaas `` Johnny '' Rep ( born 25 November 1951 in Zaandam , North Holland ) is a former Dutch footballer .", "John Nicholaas `` Johnny '' Rep ( born 25 November 1951 in Zaandam , Noord-Holland ) is a former Dutch football striker ." ]
[ "A MIXING round consists of four applications of the MIX transformation , as shown in the diagram .", "A mixing round consists of four applications of the `` mix-up '' transformation , as shown in the diagram ." ]
[ "Along with RC4 , RC2 with a 40-bit key size was treated favourably under US export regulations for cryptography .", "Along with RC4 , RC2 with a 40-bit key size was treated under US export regulations for cryptography ." ]
[ "The development of RC2 was sponsored by Lotus , who were seeking a custom cipher that , after evaluation by the NSA , could be exported as part of their Lotus Notes software .", "The development of RC2 was sponsored by Lotus , who were seeking a custom cipher be exported as part of their Lotus Notes software , a...
[ "The NSA suggested a couple of changes , which Rivest incorporated .", "The NSA suggested a couple of changes , which Ronald Rivest incorporated ." ]
[ "Its 18 rounds are arranged as a source-heavy Feistel network , with 16 rounds of one type ( MIXING ) punctuated by two rounds of another type ( MASHING ) .", "Rounds are arranged as a source-heavy feistel network , with 16 rounds of one type called `` mixing rounds '' interleaved by two rounds of another type ca...
[ "RC2 is a 64-bit block cipher with a variable size key .", "RC2 is a 64-bit block cipher with a variable key size and using 18 rounds ." ]
[ "A similar disclosure had occurred earlier with RC4 .", "A similar post had occurred earlier with RC4 ." ]
[ "In cryptography , RC2 ( also known as ARC2 ) is a symmetric-key block cipher designed by Ron Rivest in 1987 .", "In cryptography , RC2 is a symmetric-key block cipher ." ]
[ "RC2 is vulnerable to a related-key attack using 234 chosen plaintexts ( Kelsey et al. , 1997 ) .", "RC2 is susceptible to a related-key attack using 234 chosen-plaintext attacks ( Kelsey et al. , 1997 ) ." ]
[ "On November 8 , 2010 , the jury returned with a recommendation for Hayes to be executed by the State .", "On November 8 , 2010 , the jury returned with a recommendation for Hayes to be killed by the State ." ]
[ "Joshua A. Komisarjevsky ( born August 10 , 1980 ) was Hayes ' accomplice in the home invasion and murder .", "Joshua A. Komisarjevsky ( born August 10 , 1980 ) was Hayes ' accomplice in the home invasion and murder of William Petit 's wife and two daughters ." ]
[ "The Hartford Courant referred to the case as `` possibly the most widely publicized crime in the state 's history '' .", "The Hartford Courant called the case `` possibly the most widely publicized crime in the state 's history '' ." ]
[ "The Cheshire , Connecticut , home invasion murders occurred on July 23 , 2007 , when a mother and her two daughters were murdered during a home invasion in Cheshire , Connecticut .", "A mother and her two daughters were murdered during a home invasion in Cheshire , Connecticut ." ]
[ "He is incarcerated in the Northern Correctional Institution , which houses the state 's death row for men , in Somers .", "He is housed in the Northern Correctional Institution in Somers ." ]
[ "Komisarjevsky remained incarcerated at the Walker Reception Center in lieu of a $ 15 million bond until his conviction .", "Komisarjevsky was kept at the Walker Reception Center rather than pay a $ 15 million bond ." ]
[ "Over the period 1840-1843 , similar work was carried out by engineer Ludwig A. Colding though it was little known outside his native Denmark .", "Over the period 1840-1843 , similar work was carried out by engineer Ludwig A. Colding though it was little-known outside his native Denmark ." ]
[ "It was Gottfried Wilhelm Leibniz during 1676-1689 who first attempted a mathematical formulation of the kind of energy which is connected with motion ( kinetic energy ) .", "The German Gottfried Wilhelm Leibniz during 1676-1689 attempted a mathematical formulation of the kind of energy which is connected with mo...
[ "He showed that the gravitational potential energy lost by the weight in descending was equal to the internal energy gained by the water through friction with the paddle .", "He showed that the gravitational potential energy lost by the weight in descending was equal to the thermal energy ( heat ) gained by the w...
[ "In 1638 , Galileo published his analysis of several situations-including the celebrated `` interrupted pendulum '' - which can be described ( in modern language ) as conservatively converting potential energy to kinetic energy and back again .", "This can be described ( in modernized language ) as conservatively...
[ "Ancient philosophers as far back as Thales of Miletus c. ~ 550 BCE had inklings of the conservation of some underlying substance of which everything is made .", "Ancient philosophers as far back as Thales of Miletus had the idea that there is some underlying substance of which everything is made ." ]
[ "However , there is no particular reason to identify this with what we know today as `` mass-energy '' ( for example , Thales thought it was water ) .", "But that is not the same as our concept of `` mass-energy '' today ( For example , Thales thought the underlying substance was water ) ." ]
[ "Joseph Hewes ( January 23 , 1730 - November 10 , 1779 ) was a native of Princeton , New Jersey , where he was born in 1730 .", "Joseph Hewes ( January 23 , 1730 - November 10 , 1779 ) , was a native of Princeton , New Jersey , where he was born in 1730 ." ]
[ "Immediately after their marriage , they moved to New Jersey , which became Joseph Hewes 's home state .", "Immediately after their marriage they moved to New Jersey , which became Joseph Hewes 's home state ." ]
[ "Hewes moved to Edenton , North Carolina at the age of 30 and won over the people of the colony with his charm and honorable businesslike character .", "Hewes moved to Edenton , North Carolina at the age of 30 and won over the people of the state with his charm and honorable businesslike character ." ]
[ "Hewes was elected to the North Carolina legislature in 1763 , only three years after he moved to the colony .", "Hewes was elected to the North Carolina legislature in 1763 , only three years after he moved to the state ." ]
[ "After finishing his apprenticeship he earned himself a good name and a strong reputation , which would serve him well in becoming one of the most famous signers of the Declaration of Independence for North Carolina , along with William Hooper and John Penn. .", "After finishing his apprenticeship he earned himse...
[ "After being re-elected numerous times in the legislature , Hewes was now focused on a new and more ambitious job as a continental congressman .", "After being re-elected many times to the legislature , Hewes focused on a new and more ambitious job as a Continental Congressman ." ]
[ "Hewes 's parents were members of the Society of Friends , commonly known as Quakers .", "Hewes 's parents were part of the Quaker Society of Friends ." ]
[ "Bamiyan has been particularly famous for its potatoes .", "Bamiyan is famous for its potatoes ." ]
[ "Bamyan is the largest province in the Hazarajat region of Afghanistan , and is the cultural capital of the Hazara ethnic group that predominates in the area .", "Bamyan is the largest province in the Hazarajat region of Afghanistan ." ]
[ "Bamyan Province ( Pushto : بامیان Persian : بامیان ) can be translated as ` The Place of Shining Light ' ; is one of the thirty-four provinces of Afghanistan .", "Bamyan Province ( Persian : بامیان ) is one of the thirty-four provinces of Afghanistan ." ]
[ "The current governor of the province is Habiba Sarabi , Afghanistan 's first and , so far , only female governor ; she was appointed in 2005 .", "The current governor of the province is Habiba Sarabi ." ]
[ "King Crimson are a progressive rock band .", "King Crimson is a progressive rock band ." ]
[ "Based on a format of eccentric pop songs and complex instrumentals , the band recorded several unsuccessful singles and one album , The Cheerful Insanity of Giles , Giles and Fripp .", "They recorded one album called The Cheerful Insanity of Giles , Giles and Fripp ." ]
[ "The band 's debut album , In the Court of the Crimson King , was released in October 1969 on Island Records .", "Their first CD , In the Court of the Crimson King , was a huge success ." ]
[ "Later in the year King Crimson recorded and released a new album , Islands .", "King Crimson released their second album , In the Wake of Poseidon , in 1970 ." ]
[ "A Matter of Life and Death is the fourteenth studio album by British heavy metal band Iron Maiden , released on 25 August 2006 in Italy and Finland , and 28 August worldwide , excluding the US , Canada and Japan on 5 September .", "A Matter of Life and Death is an album by Iron Maiden ." ]
[ "It is named for the city of Canberra , Australia 's national capital , and includes the districts of Tuggeranong , Weston Creek and Woden Valley , along with the rest of the ACT south of the Molonglo River and Lake Burley Griffin .", "It includes the areas of Tuggeranong , Fyshwick , Weston Creek and Woden Valle...
[ "The division was created in redistibution of 19 April 1974 of the former Division of Australian Capital Territory .", "It was created in 1974 from the old Division of Australian Capital Territory ." ]
[ "Originally appeared on Fierce Panda release only .", "It appeared on the Fierce Panda version ." ]
[ "The CD single was released on 12 May 2003 .", "They made a CD single and released it on May 2003 ." ]
[ "Released version Demo version", "A demo version played on guitar was also recorded ." ]
[ "Recording took place at the Helioscentric Studios , Rye , East Sussex .", "The second one at the Helioscentric Studios in East Sussex ." ]
[ "In one last coordinated action by the Far East Air Force , U.S. planes damaged two Japanese transports , the flagship Nagato , a destroyer and sank one minesweeper .", "U.S. planes damaged two Japanese transports , the flagship Nagato , a destroyer and sank one minesweeper ." ]
[ "WPO-3 called for two defensive lines across Bataan .", "WPO-3 had two defensive lines across Bataan ." ]
[ "It was the largest surrender in American and Filipino military history , and was the largest United States surrender since the Civil War 's Battle of Harper 's Ferry .", "It was the largest United States surrender since the Civil War 's Battle of Harper 's Ferry ." ]
[ "In the face of this onslaught , the American commander , General Douglas MacArthur , realized that the beachhead defense plan had failed .", "The American commander , General Douglas MacArthur , realized that the beach defense plan had failed ." ]
[ "This forced the U.S. Asiatic Fleet to withdraw its surface ships from its naval base in Cavite and retreat southwards , leaving only the submarine force to resist the Japanese .", "The U.S. Asiatic Fleet withdrew its ships from its naval base in Cavite and retreated south ." ]
[ "The concept of WPO-3 was to delay invading Japanese forces until the U.S. Pacific Fleet could be mustered at full strength and fight its way to the Philippines .", "The plan of WPO-3 was to delay Japanese forces until the U.S. Pacific Fleet could get to the Philippines ." ]
[ "The Battle of Bataan represented the most intense phase of Imperial Japan 's invasion of the Philippines during World War II .", "The Battle of Bataan was part of Japan 's invasion of the Philippines during World War II ." ]
[ "Gen. MacArthur intended to move his men with their equipment and supplies in good order to their defensive positions .", "Gen. MacArthur wanted to move his men to defensive positions ." ]