OpenLLM-France/wikimedia huggingface dataset:
# A-level Physics (Advancing Physics)/Signal Frequencies/Worked Solutions

1. What is the frequency of an X-ray (wavelength 0.5 nm)?
X-rays are electromagnetic waves, so they travel at the speed of light (3 x 10$^8$ ms$^{−1}$).
3 x 10$^8$ = f x 0.5 x 10$^{−9}$
$f={\frac {3\times 10^{8}}{0.5\times 10^{-9}}}=600\times 10^{15}{\mbox{ Hz}}=600{\mbox{ PHz}}$
2. A sound wave, with a frequency of 44 kHz, has a wavelength of 7.7mm. What is the speed of sound?
V = 44 x 10$^3$ x 7.7 x 10$^{−3}$ = 338.8ms$^{−1}$
3. What is the fundamental frequency of the following signal?
The big spike on the left is at approximately 750 Hz, so this is the fundamental frequency.
4. Approximately how many harmonics does it contain?
There are 14 other big spikes, plus a few other spikes which may be large enough to be harmonics.
5. The three sine waves sin x°, 4sin(2x-50)° and 0.5sin(3x+120)° are added together to form a signal. What are the frequencies of each of the waves? What is the signal's fundamental frequency? Assume that the waves are travelling at the speed of light, and that 60° = 1mm
sin x° has a wavelength of 360°. Using this, we can calculate the wavelengths of the other two waves, since f(ax) stretches f(x) by the reciprocal of a on the x axis. The frequency of each wave is given by the formula:
$f={\frac {v}{\lambda \ }}={\frac {3\times 10^{8}}{\lambda \ \times 10^{-3}}}$
| Wave (y=) | Wavelength (°) | Wavelength (mm) | Frequency (GHz) |
| sin x° | 360 | 6 | 50 |
| 4sin(2x-50)° | 180 | 3 | 100 |
| 0.5sin(3x+120)° | 120 | 2 | 150 |
sin x° has the lowest frequency, so 50 GHz is the fundamental frequency of the signal.
# A-level Physics (Advancing Physics)/Semiconductors/Worked Solutions

1. What is the resistivity of silicon, at room temperature?
$\rho ={\frac {1}{\sigma }}={\frac {1}{435\times 10^{-6}}}\approx 2300\Omega {\mbox{m}}=2.3{\mbox{k}}\Omega {\mbox{m}}$
2. What sort of variable resistor would a semiconductor be useful in?
A thermistor, as the resistance of a semiconductor decreases as heat increases (but, assuming use of a potential divider, the voltmeter would have to be on the other resistor).
3. If positive ions are added to silicon (doping it), how does its conductivity change?
When a few positive ions are present, they present "holes" into which some electrons can fall. This decreases the over-all number of valence electrons in the lattice, and these are more easily occupied by drifting electrons under the application of a potential difference across the semiconductor, so the effect is greater conductivity.
# A-level Physics (Advancing Physics)/Simple Harmonic Motion/Mathematical Derivation

The following second-order differential equation describes simple harmonic motion:
${\frac {d^{2}x}{dt^{2}}}={\frac {-kx}{m}}$
${\frac {d^{2}x}{dt^{2}}}+{\frac {kx}{m}}=0$
Since we have a second derivative, we cannot separate the variables, so let:
$x=e^{zt}$
Therefore:
${\frac {dx}{dt}}=ze^{zt}$
${\frac {d^{2}x}{dt^{2}}}=z^{2}e^{zt}$
By substitution:
$z^{2}e^{zt}+{\frac {ke^{zt}}{m}}=0$
$e^{zt}\left(z^{2}+{\frac {k}{m}}\right)=0$
e$^{zt}$ is asymptotic at 0, so e$^{zt}$ cannot equal 0, and we can therefore get away with dividing by e$^{zt}$:
$z^{2}+{\frac {k}{m}}=0$
$z^{2}={\frac {-k}{m}}$
$z=\pm {\sqrt {\frac {-k}{m}}}=\pm i{\sqrt {\frac {k}{m}}}$
Therefore:
$x=Pe^{it{\sqrt {\frac {k}{m}}}}+Qe^{-it{\sqrt {\frac {k}{m}}}}$,
where P and Q are constants of integration. At this point, it is useful to clean things up a bit by letting:
$\omega ^{2}={\frac {k}{m}}$
$x=Pe^{i\omega t}+Qe^{-i\omega t}$
It has been proven elsewhere (de Moivre's Theorem) that, when n is a constant:
$e^{ni\theta }=\cos {n\theta }+i\sin {n\theta }$ and $e^{-ni\theta }=\cos {n\theta }-i\sin {n\theta }$
Therefore:
$x=P(\cos {\omega t}+i\sin {\omega t})+Q(\cos {\omega t}-i\sin {\omega t})$
$x=(P+Q)\cos {\omega t}+(P-Q)i\sin {\omega t}$
Let: $R=P+Q$
$S=P-Q$
So, the general solution of the differential equation is:
$x=R\cos {\omega t}+Si\sin {\omega t}$
This describes what the simple harmonic oscillator will do given any possible situation. However, we don't want an equation which will cover anything and everything. We want to give our oscillator a starting position - let's say, at a position where x = A at t = 0:
$A=R\cos {(\omega \times 0)}+Si\sin {(\omega \times 0)}$
$A=R\cos {0}+Si\sin {0}$
Therefore, R = A and S = 0.
So, the specific solution is:
$x=A\cos {\omega t}$
# A-level Physics (Advancing Physics)/Specific Heat Capacity

It takes energy to heat things up, since heat is work. If we heat a more massive thing up, it takes more work, because we have to give more particles, on average, an energy kT. Some substances require more work to heat up than others. This property is known as specific heat capacity. This gives us the formula:
$\Delta E=mc\Delta \theta$,
where ΔE is the work put in to heating something up (in J), m is the mass of the thing we are heating up (in kg), c is the specific heat capacity (in Jkg$^{−1}$K$^{−1}$), and Δθ is the difference in temperature due to the work done on the substance (in degrees Celsius or Kelvin). Note that some textbooks may replace ∆E with Q or q, and ∆θ with ∆T, however they represent the same concepts.
It should be noted that the specific heat capacity changes slightly with temperature, and more than slightly when the material changes state. A table of the specific heat capacities of various substances is given below:
| Substance | State | Temperature (°C) | Specific Heat Capacity (kJkg$^{−1}$K$^{−1}$) |
| Air | gas | 23 | 1.01 |
| Aluminium | solid | 25 | 0.90 |
| Animal (and human) tissue | mixed | 25 | 3.5 |
| Argon | gas | 25 | 0.52 |
| Copper | solid | 25 | 0.39 |
| Glass | solid | 25 | 0.84 |
| Helium | gas | 25 | 5.19 |
| Hydrogen | gas | 25 | 14.3 |
| Iron | solid | 25 | 0.45 |
| Lead | solid | 25 | 0.13 |
| Nitrogen | gas | 25 | 1.04 |
| Oxygen | gas | 25 | 0.92 |
| Uranium | solid | 25 | 0.12 |
| Water | solid | -10 | 2.05 |
| Water | liquid | 25 | 4.18 |
| Water | gas | 100 | 2.08 |

## Questions

1. How much work would it take to heat 100 kg of liquid water from 20 °C to 36.8 °C?
2. How much work would it take to heat a well-insulated room from 15 °C to 21 °C, if the room is a cube with side length 10m, and the density of the air is 1.2kgm$^{−3}$?
3. A 10 kg block of iron at 80 °C is placed in the room above once it has reached 21 °C. If the iron cools by 40 °C, what is the new temperature of the room?
Worked Solutions
# A-level Physics (Advancing Physics)/Simple Harmonic Motion/Worked Solutions

1. A 10N weight extends a spring by 5 cm. Another 10N weight is added, and the spring extends another 5 cm. What is the spring constant of the spring?
$\Delta F=k\Delta x$
$10=0.05k$
So $k={\frac {10}{0.05}}=200Nm^{-1}$
2. The spring is taken into outer space, and is stretched 10 cm with the two weights attached. What is the time period of its oscillation?
First calculate the mass of the two weights:
$20=9.81m$
m = 2.04 kg
$T=2\pi {\sqrt {\frac {m}{k}}}=2\pi {\sqrt {\frac {2.04}{200}}}=0.634{\mbox{ s}}$
3. What force is acting on the spring after 1 second? In what direction?
We are starting the oscillation at t=0 with a displacement. This displacement is the amplitude of the oscillation, and we need f(ωt) to be positive at t=0. So, we use an equation for the displacement with a cosine in it. We have already derived the acceleration in this case:
$a=-\omega ^{2}\cos {\omega t}$
$\omega ={\frac {2\pi }{T}}={\frac {2\pi }{6.34}}=0.99{\mbox{ rad s}}^{-1}$
So:
$a=-0.99^{2}\cos {0.99\times t}=-0.538{\mbox{ ms}}^{-2}$
The minus sign means that the acceleration is in the opposite direction to the initial displacement.
4. A pendulum oscillates with a frequency of 0.5 Hz. What is the length of the pendulum?
$\omega =2\pi f$
${\sqrt {\frac {g}{l}}}=2\times \pi \times 0.5$
${\sqrt {\frac {9.81}{l}}}=\pi$
${\frac {9.81}{l}}=\pi ^{2}$
$l={\frac {9.81}{\pi ^{2}}}=0.994{\mbox{ m}}$
5. The following graph shows the displacement of a simple harmonic oscillator. Draw graphs of its velocity, momentum, acceleration and the force acting on it.
x is a sine wave, so:
$x=A\sin {\omega t}$
$v={\frac {dx}{dt}}=A\omega \cos {\omega t}$
$a={\frac {dv}{dt}}={\frac {d^{2}x}{dt^{2}}}=-A\omega ^{2}\sin {\omega t}$
$p=mv=mA\omega \cos {\omega t}$
$F=ma=-mA\omega ^{2}\sin {\omega t}$
Since you haven't been given any details, the amplitudes of the waves don't matter. The phase differences, however, do.
6. A pendulum can only be modelled as a simple harmonic oscillator if the angle over which it oscillates is small. Why is this?
Simple harmonic oscillators work because the force acts in the opposite direction to the displacement. As the pendulum moves away from the area immediately below the peg it is hanging on, the force no longer acts in the opposite direction to the displacement.
# Adventist Youth Honors Answer Book/Knot/Square

* Square Knot
* Use: Also known as a Reef knot, the Square Knot is easily learned and useful for many situations. It is most commonly used to tie two lines together at the ends. This knot is used at sea in reefing and furling sails. It is used in first aid to tie off a bandage or a sling because the knot lies flat.
* How to tie:
* Pass left end over and under right end.
* Curve what is now the left end toward the right and cross what is now the right end over and under the left.
* Draw up tight by pulling one end and line away from the other end and line.
* WARNING: Do not rely on this knot to hold weight in a life or death situation. It has been known to fail.
# Adventist Youth Honors Answer Book/Knot/Pipe hitch

* Pipe hitch
* Use: The pipe hitch is used for hoisting tubular objects (such as pipes).
* How to tie:
* Make four or five turns around the pipe with the rope.
* Bring the running end back to the standing part.
* Tie two half-hitches around the standing part.
# Adventist Youth Honors Answer Book/Knot/Prusik

* Prusik knot
* Use: A Prusik (aka Prussik or Prussic) is a friction hitch used in climbing, canyoneering, caving, rope rescue and by arborists to grab a rope (sometimes referred to as a rope-grab). The term Prusik is used both for the knot, for the loops of cord, and for the action (to prusik).
* A Prusik rope is a circular loop with a circumference of 20 to 100 cm depending on its intended use. Two Prusik ropes are tied to another rope which is anchored above. When the Prusik knot is under tension, it grabs the rope to which it is tied. When not under tension, it is easily moved. The climber places one foot into each loop, and shifts all of his or her weight to one of them, releasing the tension on the other. The rope without tension is then slid upwards on the vertical rope. The climber the shifts his or her weight to the other loop and slides the first one up. This is repeated until the rope has been ascended.
* Prusiks will work around two ropes, even two ropes of different diameters. Prusiks provide a high-strength and relatively fail-safe (i.e., they will slip before damaging the rope or breaking) attachment, and are used in some rope-rescue techniques. Prusiks are good to use in hauling systems where multiple rope-grabs may be needed, and where mechanical rope-grabs are not available.
* Although the Prusik Climb technique may be called old-school by some, the US Army still includes it in its annual Best Ranger competition. Rangers in the competition routinely make it up a 90 foot rope in under a minute.
* How to tie:
* The Prusik is tied by wrapping the prusik loop around the rope a number of times (depending on the materials, but usually 3-5 times), and then back through itself, forming a barrel around the rope, with a tail hanging out the middle. When the tail is weighted the turns tighten around the main rope and grab. When weight is removed the loop can be slid along the rope by placing a hand directly on the barrel and pushing. The trick is, if it grabs well, then it is hard to slide along the rope. Breaking the Prusik free from the rope after it has been weighted can be difficult, and is easiest done by pushing the bow, being the loop of cord which runs from the top wrap, over the knot to the bottom wrap, along the tail a little. This loosens the grip of the hitch and makes movement easier.
* Step 1
* Step 2
* Step 3
* Step 4
* Locked while holding tension.
* Slides readily without tension.
# Adventist Youth Honors Answer Book/Knot/Slipped sheet bend

* Slipped sheet bend
* Use: The slipped sheet bend is used in non-critical situations for temporarily joining two ropes.
* How to tie:
* Start the same as in tying a regular sheet bend, only pass a bight (light blue in the illustration) under the last rope (dark blue) instead of passing the running end under.
* WARNING: The slightest tug on the running end will untie this knot instantly - even if the knot is under load.
# Adventist Youth Honors Answer Book/Knot/Ring Bend Knot

* Ring Bend (Water Knot, Tape Knot)
* Use: The water knot (or tape knot) is a knot frequently used in climbing for joining two ends of webbing together, for instance when making a sling.
* The ends should be left at least three inches long and the knot should be "set" by tightening it with full body weight. The ends can be taped or lightly sewn to the standing parts to help prevent them from creeping back into the knot. Inspect the knot before each use.
* How to tie:
* To tie, first form an overhand knot in one end and then follow it with the other end, feeding in the opposite direction.
# Adventist Youth Honors Answer Book/Knot/Sheetbend

* Sheetbend
* Use: The sheet bend knot is excellent for joining two ropes together, especially if the two ropes are not the same size. When tied properly, it will not come undone, and it is easy to untie. It is very similar to the bowline.
* How to tie:
* Make a bight at the end of the larger rope (if they are not the same size).
* Run the end of the smaller rope through the bight, entering from the bottom.
* Wrap the end of small rope around the back of the large rope, crossing the short end of the large rope first.
* Tuck the end of the short rope under itself, on top of the bight.
# Adventist Youth Honors Answer Book/Knot/Packer's

* Packer's knot
* Use: The Packer's Knot is a binding knot usually used in smaller line.
* This knot is sometimes used in baling and in parcel tying.
* How to tie:
* Make a figure eight not near the standing end of the rope. Wrap the running end around the "parcel" and pass it through the top loop of the "eight" following the same path as standing end.
* Make a loop in the running end and pass the standing end through it.
* Tighten.
# Adventist Youth Honors Answer Book/Knot/Sheepshank

* Sheepshank
* Use: The sheepshank knot is used to shorten a length of rope. It comes undone easily unless it is under tension.
* WARNING: Keep this knot under tension or it will come untied.
# Adventist Youth Honors Answer Book/Knot/Slip

* Slip knot
* Use: A slip knot is one that will tighten under load, and which can be easily untied by pulling on the running end. This knot is typically a component of more complicated knots, and is generally not used by itself.
* How to tie:
* A slip knot can be tied by starting an overhand knot, but instead of passing the running end through the loop, pass a bight through instead.
* WARNING: If tied as shown in the illustration, the running end (on the right) will pull through the loop if even the slightest load is applied to the standing end (on the left). If one reverses the standing end and running ends in the illustration, the knot is far more stable. As shown, the knot will hold a load on the running end, but not on the standing end.
# Adventist Youth Honors Answer Book/Knot/Slipped half hitch

* Slipped half-hitch
* Use: A slipped half-hitch is a knot used to attach a line to a rod or bar. It does not provide great strength compared to some other knots, but it can be tied relatively quickly and released very easily. These characteristics mean that it is used on square-rigged ships for securing the gaskets that bind stowed sails to the yards.
* How to tie:
* Begin as for a clove hitch, but instead of passing the end of the line through the loop in the final step, pass a bight instead, leaving the end on the original side. Pulling on this end will release the hitch - if tied in a gasket, this will quickly release the sail.
* WARNING: Never use this knot in a critical situation. It comes untied at the slightest provocation.
# Ada Programming/Attributes/'Component Size
## Description

R'Component_Size is a representation attribute used to get the number of bits of each component of an array object or type.
The 'Component_Size attribute may also be used in representation clauses to specify the size in bits used to store each component of an array type.

## See also
### Wikibook

* Ada Programming
* Ada Programming/Attributes
* Ada Programming/Attributes/'Size
* Ada Programming/Attributes/'Max_Size_In_Storage_Elements
* Ada Programming/Attributes/'Value_Size (implementation defined)
* Ada Programming/Attributes/'Object_Size (implementation defined)

### Ada 95 Reference Manual

* 13.3: Operational and Representation Attributes
* Annex K: Language-Defined Attributes

### Ada 2005 Reference Manual

* 13.3: Operational and Representation Attributes
* Annex K: Language-Defined Attributes
# Ada Programming/Attributes/'Copy Sign
## Description

S'Copy_Sign(X, Y) is an Ada attribute where S is any floating-point type, and X and Y are any instance of that type. This attribute represents the floating point value with the magnitude of X and the sign of Y.
If the resulting value is outside the base range of S, a Constraint_Error exception is raised.

## See also
### Wikibook

* Ada Programming
* Ada Programming/Attributes

### Ada Reference Manual

* A.5.3 Attributes of Floating Point Types (Annotated)
* Annex K Language-Defined Attributes (Annotated)
# Ada Programming/Attributes/'Count
## Description

X'Count is an Ada attribute where X is an entry point in a protected type. This attribute returns the number of tasks currently enqueued waiting for entrance into the entry procedure.

## See also
### Wikibook

* Ada Programming
* Ada Programming/Tasking

### Ada Reference Manual

* 13.3 Operational and Representation Attributes (Annotated)
* Annex K Language-Defined Attributes (Annotated)
# Ada Programming/Attributes/'Class

The Class attribute denotes the class wide type of the given tagged type.

## See also
### Wikibook

* Ada Programming
* Ada Programming/Object Orientation
* Ada Programming/OO

### Ada Reference Manual

* 3.9 Tagged Types and Type Extensions (Annotated)
* 7.3.1 Private Operations (Annotated)
# Ada Programming/Attributes/'Code Address
## Description

The 'Address attribute may be applied to subprograms in Ada 95 and Ada 2005, but the intended effect seems to be to provide an address value which can be used to call the subprogram by means of an address clause as in the following example:
A call to L is then expected to result in a call to K. In Ada 83, where there were no access-to-subprogram values, this was a common work-around for getting the effect of an indirect call. GNAT implements the above use of Address and the technique illustrated by the example code works correctly.
However, for some purposes, it is useful to have the address of the start of the generated code for the subprogram. On some architectures, this is not necessarily the same as the Address value described above. For example, the Address value may reference a subprogram descriptor rather than the subprogram itself.
The 'Code_Address attribute, which can only be applied to subprogram entities, always returns the address of the start of the generated code of the specified subprogram, which may or may not be the same value as is returned by the corresponding 'Address attribute.
# Ada Programming/Attributes/'Compose
## Description

X'Compose(Fraction : X, Exponent : Integer) is an Ada attribute where X is any floating point type.
Floating point types are represented as:
    $sign\times mantissa\times radix^{exponent}$
where
    sign is 1 or -1
    mantissa is a fraction in base radix
    radix is the hardware radix (usually 2)
    exponent is an integer
'Compose(Fraction, Exponent) returns the floating point number Fraction with the exponent replaced with Exponent.

## Example

The output with GNAT 4.6 on the x86-64 architecture is:

## See also
### Wikibook

* Ada Programming
* Ada Programming/Attributes
* Ada Programming/Attributes/'Fraction

### Ada Reference Manual

* 5.3 Attributes of Floating Point Types (Annotated)
* Annex K Language-Defined Attributes (Annotated)
# Ada Programming/Attributes/'Constrained
## Description

True if A of discriminated type denotes a constant, a value, or a constrained variable.
Yields the value True if A denotes a constant, a value, a tagged object, or a constrained variable, and False otherwise.
The value of this attribute is of the predefined type Boolean.
# Ada Programming/Attributes/'Ceiling
## Description

X'Ceiling(Y) is an Ada attribute where X is any floating-point type and Y is any instance of that type. This attribute represents the smallest integer value that is greater than or equal to Y.

## See also
### Wikibook

* Ada Programming
* Ada Programming/Attributes
* Ada Programming/Attributes/'Floor
* Ada Programming/Attributes/'Rounding
* Ada Programming/Attributes/'Unbiased_Rounding

### Ada Reference Manual

* 13.3 Operational and Representation Attributes (Annotated)
* Annex K Language-Defined Attributes (Annotated)
# Ada Programming/Attributes/'Compiler Version
## Description

Standard'Compiler_Version (Standard is the only allowed prefix) yields a static string identifying the version of the compiler being used to compile the unit containing the attribute reference.
# Ada Programming/Attributes/'Caller
## Description

Identifies the task whose call is now being serviced. Yields a value of the type Task_Id that identifies the task whose call is now being serviced.
Use of this attribute is allowed only inside an accept_statement, or entry_body after the entry_barrier, corresponding to the entry_declaration denoted by E.
# Annotated Republic of China Laws/Criminal Code of the Armed Forces/Article 79

| ←Article 75 to Article 78 | Criminal Code of the Armed Forces Republic of China Law Article 79 | Article 80 to Article 119→ |

## Promulgated complete amendment on 2001-09-28

Effective on 2001-10-02

### Article 79

    This Code will be put into effect on October 2, 2001.

## Promulgated amendment on 2007-12-12
### Article 79

    This Code will be put into effect on the date of its promulgation, except for Articles which were amended and promulgated on Sept. 28, 2001 and took effect on Oct. 2, 2001.
* ↑ Reversed-derived from 2007 text.
* ↑ "Criminal Code of the Armed Forces: Article 79". Laws & Regulations Database of The Republic of China. Ministry of Justice (Taiwan). 2017-04-19. Retrieved 2019-11-21.