itisarainyday/ml_classifier_bert_training · Datasets at Hugging Face

0 stringlengths 10 969	label int64 0 1
These discs were latex5 diameter and the centers of the holes were latex6 apart.	0
The change in specific exergy flow rate of the steam flowing into and out of the turbine.	0
Define latex0 : If latex1 and latex2 are both real, find latex1 .	1
Now suppose that the boiler is able to superheat the steam, to a boiler exit / turbine inlet temperature latex7 of latex8 .	0
When the rod rotates fast enough, the bearing breaks.	1
Its binary representation is latex105 , wherein the sequence latex48 is repeated \_ad infinitum}.	0
State whether the the bed shear stresses computed in Part (a) and Part (b) should be the same or not.	1
Calculate the exit velocity latex0 .	1
Using dimensional analysis find the non-dimensional parameters which govern this observed behavior.	1
The chain is required because the engine's output shaft is connected to a sprocket and the belt is required to allow for slip.	0
How long does a pendulum need to be to have a frequency of latex7 ?	1
Show that the latex10 -component of the velocity is zero everywhere in the gap.	1
The functions are referred to as (Square), (Triangle) and (Parabola) in the solutions.	0
All this implies, for the real plant, an increase in fuel consumption and an increase in size and cost.	0
Show that: latex3 Use your result to part (a) to find an expression for latex4 for an initial Gaussian temperature distribution: latex5	1
Consider the direction of the flow (to the right) as positive.	1
The wheel is a uniform disc of diameter latex1 and mass latex2 .	0
With the system at rest.	0
(L8): Use Gaussian elimination to find the intersection between the line latex0 and the plane latex1 .	1
The enzyme lactate dehydrogenase catalyses the reaction: latex0 The progress of the reaction can be monitored by measuring the rate at which latex1 is produced spectrophotometrically, using the Beer-Lambert law: latex2 * latex3 Absorbance (dimensionless) * latex4 Molar absorption coefficient.	0
Find the height latex7 reached by the ball after its first bounce and the corresponding drop time latex8 .	1
If latex0 and latex1 and latex2 are related to two new independent variables latex3 and latex4 by latex5 so that latex6 , Use the chain rule to find latex7 and latex8 in terms of latex9 and latex10 .	1
The wall is of thickness latex1 and of thermal conductivity latex2 .	0
(Hint: Find the new normal vector of the solar panel.)	1
The internal forces cancel out.	0
The clinometer is held exactly latex1 above the ground.	0
That one regenerated latex0 molecule can then re-enter the Q cycle again (note the halving of all the terms): latex17 And the ‘half a molecule of latex0 regenerated by this can re-re-enter the Q-cycle too: latex19 And so on.	0
Sketch the output waveform at point "P", showing voltage and time scales, whilst this voltage is applied.	1
How many units of enzyme were present per millilitre of the lactate dehydrogenase solution?	1
In this problem, we will consider some practical applications of the Fourier transform in optics.	0
Consider a solar power plant.	0
* The distance between points latex0 and latex5 is latex9 * The distance between points latex0 and latex3 is latex12 Find the time, latex13 , required for the axle to complete a revolution about latex0 and the direction of this rotation.	1
(lamina = thin sheet) Find the area the ellipse encloses.	1
Give your answer to 1 decimal place.	1
(L9): Consider the matrices: latex0 Calculate the following, and state in words the property being demonstrated in each part, e.g "associative" or "non- associative".	1
The other end may be supported by one of the following methods (see parts (a)-(e)).	0
latex8 [table] Using the life fraction rule, calculate the creep damage fraction accumulated in a week.	1
Assuming that the height difference latex4 is initially zero, how long will it take for the mass to be dislodged?	1
You are now tasked with building a go-kart capable of travelling at a max speed of between 12 and 14 m/s.	0
Show that latex0 where latex1 is a constant and latex2 .	1
We are going to test a latex8 scale model of a latex9 long ship.	0
iii) latex8 ?	1
The transistor is of 2N 3055 type, with an latex1 of latex2 , and the motor’s operating voltage is latex3 .	0
However, the equation is actually a linear second order ODE hence analysis is simpler.	0
Calculate the total heads of water at the sea, the lake and at Point 3.	1
Does Matt receive the two light pulses simultaneously?	1
This allows you to calculate the cell growth rate, latex3 , from a graph.	0
A tornado cruising over the ocean suddenly receives an alert signal of being under attack from a missile.	0
Hence convert this into Cartesian form.	1
Given the definitions (in lectures) of the hyperbolic functions latex0 , latex1 and latex2 , show that: latex3 latex4 latex5 latex6	1
A 5 kg mass moves under the influence of a time-dependent force latex0 N, where latex1 is the time in seconds.	0
Using the average value of latex5 and modelling only the bed boundary condition, give the solution to this problem.	1
Calculate the angular frequencies, latex1 and latex2 , of the two normal modes.	1
Use the transformation matrix to transform all of the points found after the first rotation.	1
Consider the y-momentum equation (13.3) from Lecture 13, applied to a non-parallel channel (illustrated): latex0 and the following dimensionless groups: latex1 Non-dimensionalise the y-momentum equation and identify the order of magnitude of each term.	1
For the network shown below: Calculate the voltage latex0 (remember that, unless otherwise stated, latex0 means the voltage relative to ground).	1
Make sure you take into account the unit quantities.	0
Determine which of the following are exact differentials: latex0 latex1 latex2 latex3 latex4	1
Assuming that latex3 starts at the negative op-amp source voltage latex5 , the switching point when latex3 becomes latex7 occurs when the voltage at node “a” is equal to latex8 (i.e latex9 ), which we will call latex10 .	0
Show that the torque latex3 exerted on the rod and masses by the axle is given by latex4 It is easiest to work in a coordinate system with the origin at the bearing and the latex5 axis along the axle.	1
The length of the track from latex4 to latex5 is latex6 and the car has a mass of latex7 .	0
One stream has a constant flow latex2 and the outflowing stream should be latex3 .	0
Hence show that latex4	1
Both scripts are provided in both MATLAB and Python.	0
Square wave inputs of latex1 and latex2 respectively, from sources of very low input impedance, are applied at points A and B as shown: From first principles, derive the expression for a summing amplifier described in Section 5.7.1 of the lecture notes.	1
The shear stress at the interface of the water and oil is latex13 .	0
Hence find the clock period latex21 in this frame.	1
Starting from Navier-Stokes equations in cylindrical coordinates, derive an equation that describes the axial component of the oil/water velocity.	1
The collar shown can slide without friction on a fixed vertical guide.	0
Note that the buffer is also resistant to change below latex14 and above latex15 : this is 'pseudo-buffering', and merely due to the fact that very acidic solutions are resistant to latex1 change purely because they contain very high concentrations of latex17 or latex18 .	0
The fin is a cantilever, i.e it is fixed at one end and free at the other end.	0
(Note: there is no response area for this question.	0
latex1 , to obtain an expression for latex0 in terms of latex40 *.	0
What is the maximum range when latex3 ?	1
The strip is latex1 long, with a cross-section latex2 by latex3 , and is pin-jointed at both ends.	0
What is the net wave drag of this configuration at the design Mach number?	1
Sketch the graph of the function in latex4 .	1
Estimate the settling velocity.	1
Air ( latex0 ) is flowing isentropically in a channel.	0
Plot the following numbers in the complex plane (Argand diagram): latex0 latex1 latex2 latex3	1
Blood flow in the heart is Flow in a river is Water flow from a tap Flow in a vein	0
An acoustic wave in the water, with a wavelength much larger than the bubble, excites the bubble into an oscillating motion (compressing and expanding) at a steady frequency latex1 with an amplitude, latex2 , that is small relative to the bubble radius ( latex3 ).	0
The sand disposal is characterised by a medium sediment size latex2 .	0
\[Note: for exponents, use \\ instead of ^. ]	0
The flow is uniform along the plate (i.e along latex2 and latex3 coordinates as shown in the image) and the ambient pressure latex4 is uniform and constant.	0
What observation did we make about the boundary layer to start the approximation?	1
For a narrow channel ( latex2 ) and moderate Reynolds number ( latex3 ) which terms can be neglected and which terms are the highest order?	1
Its polar equation is latex0 where latex1 and latex2 .	0
BONUS QUESTION (to think about...) Can you think of a way to use the result shown in part (c) to construct a parabola with a given target, axis and range?	1
What will be the voltage at the op-amp’s inverting input?	1
Take latex16 .	0
The mean radius and axial velocity are constant.	0
Controlled fusion is challenging because the positively charged nuclei must overcome their electrostatic repulsion such that the strong force takes over and they fuse.	0
\[Riley 11.26] A vector field latex0 is defined in cylindrical polar coordinates latex1 by latex2 Calculate, as a surface integral, the flux of latex0 through the closed surface bounded by the cylinders latex4 and latex5 and the planes latex6 .	0
* Show that the pressure in the water is: latex7 where latex8 is a constant.	1
Solve this using the trial solution latex11 , where latex12 is a complex amplitude to find the unknown parameters latex13 and latex14 .	1
Two strain gauges are fitted at latex0 to the axis of a latex1 diameter steel shaft.	0
Construct the integral solution to the 1-D diffusion equation of a contaminant with initial concentration latex0 Starting from the fundamental solution for an instantaneous point release, show that the integral can be evaluated to give latex1 Hint: make a change of variables latex2 to solve the integral.	1
Find latex9 , latex10 , latex11 , latex12 , and latex13 .	1
The pressure force in a hydrostatic fluid is a vector given by latex0 .	0

These discs were latex5 diameter and the centers of the holes were latex6 apart.

0

The change in specific exergy flow rate of the steam flowing into and out of the turbine.

0

Define latex0 : If latex1 and latex2 are both real, find latex1 .

1

Now suppose that the boiler is able to superheat the steam, to a boiler exit / turbine inlet temperature latex7 of latex8 .

0

When the rod rotates fast enough, the bearing breaks.

1

Its binary representation is latex105 , wherein the sequence latex48 is repeated \_ad infinitum}.

0

State whether the the bed shear stresses computed in Part (a) and Part (b) should be the same or not.

1

Calculate the exit velocity latex0 .

1

Using dimensional analysis find the non-dimensional parameters which govern this observed behavior.

1

The chain is required because the engine's output shaft is connected to a sprocket and the belt is required to allow for slip.

0

How long does a pendulum need to be to have a frequency of latex7 ?

1

Show that the latex10 -component of the velocity is zero everywhere in the gap.

1

The functions are referred to as (**Square**), (**Triangle**) and (**Parabola**) in the solutions.

0

All this implies, for the real plant, an increase in fuel consumption and an increase in size and cost.

0

Show that: latex3 Use your result to part (a) to find an expression for latex4 for an initial Gaussian temperature distribution: latex5

1

Consider the direction of the flow (to the right) as positive.

1

The wheel is a uniform disc of diameter latex1 and mass latex2 .

0

With the system at rest.

0

**(L8)**: Use Gaussian elimination to find the intersection between the line latex0 and the plane latex1 .

1

The enzyme lactate dehydrogenase catalyses the reaction: latex0 The progress of the reaction can be monitored by measuring the rate at which latex1 is produced spectrophotometrically, using the Beer-Lambert law: latex2 * latex3 Absorbance (dimensionless) * latex4 Molar absorption coefficient.

0

Find the height latex7 reached by the ball after its first bounce and the corresponding drop time latex8 .

1

If latex0 and latex1 and latex2 are related to two new independent variables latex3 and latex4 by latex5 so that latex6 , Use the chain rule to find latex7 and latex8 in terms of latex9 and latex10 .

1

The wall is of thickness latex1 and of thermal conductivity latex2 .

0

(**Hint:** Find the new normal vector of the solar panel.)

1

The internal forces cancel out.

0

The clinometer is held exactly latex1 above the ground.

0

That one regenerated latex0 molecule can then re-enter the Q cycle again (note the halving of all the terms): latex17 And the ‘half a molecule of latex0 regenerated by this can re-re-enter the Q-cycle too: latex19 And so on.

0

Sketch the output waveform at point "P", showing voltage and time scales, whilst this voltage is applied.

1

How many units of enzyme were present per millilitre of the lactate dehydrogenase solution?

1

In this problem, we will consider some practical applications of the Fourier transform in optics.

0

Consider a solar power plant.

0

* The distance between points latex0 and latex5 is latex9 * The distance between points latex0 and latex3 is latex12 Find the time, latex13 , required for the axle to complete a revolution about latex0 and the direction of this rotation.

1

(lamina = thin sheet) Find the area the ellipse encloses.

1

Give your answer to 1 decimal place.

1

**(L9)**: Consider the matrices: latex0 Calculate the following, and state in words the property being demonstrated in each part, e.g "associative" or "non- associative".

1

The other end may be supported by one of the following methods (see parts (a)-(e)).

0

latex8 [table] Using the life fraction rule, calculate the creep damage fraction accumulated in a week.

1

Assuming that the height difference latex4 is initially zero, how long will it take for the mass to be dislodged?

1

You are now tasked with building a go-kart capable of travelling at a max speed of between 12 and 14 m/s.

0

Show that latex0 where latex1 is a constant and latex2 .

1

We are going to test a latex8 scale model of a latex9 long ship.

0

iii) latex8 ?

1

The transistor is of 2N 3055 type, with an latex1 of latex2 , and the motor’s operating voltage is latex3 .

0

However, the equation is actually a linear second order ODE hence analysis is simpler.

0

Calculate the total heads of water at the sea, the lake and at Point 3.

1

Does Matt receive the two light pulses simultaneously?

1

This allows you to calculate the cell growth rate, latex3 , from a graph.

0

A tornado cruising over the ocean suddenly receives an alert signal of being under attack from a missile.

0

Hence convert this into Cartesian form.

1

Given the definitions (in lectures) of the hyperbolic functions latex0 , latex1 and latex2 , show that: latex3 latex4 latex5 latex6

1

A 5 kg mass moves under the influence of a time-dependent force latex0 N, where latex1 is the time in seconds.

0

Using the average value of latex5 and modelling only the bed boundary condition, give the solution to this problem.

1

Calculate the angular frequencies, latex1 and latex2 , of the two normal modes.

1

Use the transformation matrix to transform all of the points found after the first rotation.

1

Consider the y-momentum equation (13.3) from Lecture 13, applied to a non-parallel channel (illustrated): latex0 and the following dimensionless groups: latex1 Non-dimensionalise the y-momentum equation and identify the order of magnitude of each term.

1

For the network shown below: Calculate the voltage latex0 (remember that, unless otherwise stated, latex0 means the voltage relative to ground).

1

Make sure you take into account the unit quantities.

0

Determine which of the following are exact differentials: latex0 latex1 latex2 latex3 latex4

1

Assuming that latex3 starts at the negative op-amp source voltage latex5 , the switching point when latex3 becomes latex7 occurs when the voltage at node “a” is equal to latex8 (i.e latex9 ), which we will call latex10 .

0

Show that the torque latex3 exerted on the rod and masses by the axle is given by latex4 It is easiest to work in a coordinate system with the origin at the bearing and the latex5 axis along the axle.

1

The length of the track from latex4 to latex5 is latex6 and the car has a mass of latex7 .

0

One stream has a constant flow latex2 and the outflowing stream should be latex3 .

0

Hence show that latex4

1

Both scripts are provided in both MATLAB and Python.

0

Square wave inputs of latex1 and latex2 respectively, from sources of very low input impedance, are applied at points A and B as shown: From first principles, derive the expression for a summing amplifier described in Section 5.7.1 of the lecture notes.

1

The shear stress at the interface of the water and oil is latex13 .

0

Hence find the clock period latex21 in this frame.

1

Starting from Navier-Stokes equations in cylindrical coordinates, derive an equation that describes the axial component of the oil/water velocity.

1

The collar shown can slide without friction on a fixed vertical guide.

0

Note that the buffer is also resistant to change below latex14 and above latex15 : this is 'pseudo-buffering', and merely due to the fact that very acidic solutions are resistant to latex1 change purely because they contain very high concentrations of latex17 or latex18 .

0

The fin is a cantilever, i.e it is fixed at one end and free at the other end.

0

(**Note**: there is no response area for this question.

0

latex1 , to obtain an expression for latex0 in terms of latex40 *.

0

What is the maximum range when latex3 ?

1

The strip is latex1 long, with a cross-section latex2 by latex3 , and is pin-jointed at both ends.

0

What is the net wave drag of this configuration at the design Mach number?

1

Sketch the graph of the function in latex4 .

1

Estimate the settling velocity.

1

Air ( latex0 ) is flowing isentropically in a channel.

0

Plot the following numbers in the complex plane (Argand diagram): latex0 latex1 latex2 latex3

1

Blood flow in the heart is Flow in a river is Water flow from a tap Flow in a vein

0

An acoustic wave in the water, with a wavelength much larger than the bubble, excites the bubble into an oscillating motion (compressing and expanding) at a steady frequency latex1 with an amplitude, latex2 , that is small relative to the bubble radius ( latex3 ).

0

The sand disposal is characterised by a medium sediment size latex2 .

0

\[Note: for exponents, use \*\* instead of ^. ]

0

The flow is uniform along the plate (i.e along latex2 and latex3 coordinates as shown in the image) and the ambient pressure latex4 is uniform and constant.

0

What observation did we make about the boundary layer to start the approximation?

1

For a narrow channel ( latex2 ) and moderate Reynolds number ( latex3 ) which terms can be neglected and which terms are the highest order?

1

Its polar equation is latex0 where latex1 and latex2 .

0

BONUS QUESTION (to think about...) Can you think of a way to use the result shown in part (c) to construct a parabola with a given target, axis and range?

1

What will be the voltage at the op-amp’s inverting input?

1

Take latex16 .

0

The mean radius and axial velocity are constant.

0

Controlled fusion is challenging because the positively charged nuclei must overcome their electrostatic repulsion such that the strong force takes over and they fuse.

0

*\[Riley 11.26]* A vector field latex0 is defined in cylindrical polar coordinates latex1 by latex2 Calculate, as a surface integral, the flux of latex0 through the closed surface bounded by the cylinders latex4 and latex5 and the planes latex6 .

0

* Show that the pressure in the water is: latex7 where latex8 is a constant.

1

Solve this using the trial solution latex11 , where latex12 is a complex amplitude to find the unknown parameters latex13 and latex14 .

1

Two strain gauges are fitted at latex0 to the axis of a latex1 diameter steel shaft.

0

Construct the integral solution to the 1-D diffusion equation of a contaminant with initial concentration latex0 Starting from the fundamental solution for an instantaneous point release, show that the integral can be evaluated to give latex1 Hint: make a change of variables latex2 to solve the integral.

1

Find latex9 , latex10 , latex11 , latex12 , and latex13 .

1

The pressure force in a hydrostatic fluid is a vector given by latex0 .

0