OpenLLM-France/wikimedia huggingface dataset:
# HSC Physics/Core/Motors and Generators/Generating electricity/Notes/Eddy currents and applications
## Applications of eddy currents
### Induction cooktops

An induction cooktop has a coil wound on ferromagnetic material under it. A high frequency alternating current in this coil produces a rapidly changing magnetic field. Placing a magnetic-based leads to a change in magnetic flux, because the magnetic field B varies. From Faraday's Law, ${\mathcal {E}}={\frac {\Delta \phi }{\Delta t}},$ an emf (electromagnetic field) is induced. From Lenz's Law, eddy currents flow in the pan. The resistance in the pan to the oscillating AC current results in heat being produced directly in the base of the pan. Unlike gas cooking, the ceramic cooktop is not heated directly. This makes induction cookers much more energy efficient than traditional cookers.
The direction of the eddy current is determined by Lenz's Law. In addition to efficiency, other benefits include safety (because the cooktop is not heated directly) and speed of cooking.

### Electromagnetic braking

When a rotating metal disc passes through a magnetic field, there is a change in magnetic flux. From Faraday's Law, an emf is induced. From Lenz's Law, this induces eddy currents whose magnetic field interacts with the external magnetic field in a way that causes in magnetic flux in the disk. That is, the currents inside the magnetic field experience a force that acts in the opposite direction to the motion of the disc. Therefore, the speed of the disc's motion slows down.
One benefit of electromagnetic braking is that the braking is smooth. This is because the strength of the eddy currents is proportional to the speed of the disc. This means as the disc slows, eddy currents reduce. There is no physical contact between the disc and brake. Another benefit is that it is more effiecient at high speeds because the opposing magnetic forces is larger at higher speeds. These useful properties of electromagnetic brakes serve them well in many applications, such as amusement park ride brakes and brakes in some types of trains.
# HSC Physics/Core/Motors and Generators/Generating electricity
## Notes

* Eddy currents and applications

## Questions

* Mathematical problems
* Multiple choice
* Written responses
# HSC Mathematics Advanced, Extension 1, and Extension 2/3-Unit/HSC/Induction

Induction is a form of proof useful for proving equations involving non-closed expressions (i.e., expressions with $n$ terms; sequences).

## Explanation

Induction involves first proving that the equation is true for $n=1$, then proving true for $n=k+1$ (assuming for the purpose of the proof that the equation holds true for $n=k$). Since it is true for $n=k$ and true for $n=k+1$, and also true for $n=1$, it is true for $n=2$. It follows that it is true for all positive integers $n$.

### Examples
#### Proving the formula for the sum of a series

Q: Prove by mathematical induction that for all integers $n\geq 1$,
    $1^{3}+2^{3}+3^{3}+4^{3}+\cdots +n^{3}=(1+2+3+....n)^{2}$
A:
* When $n=1$, $1^{3}=1={\tfrac {1}{4}}(1)^{2}((1)+1)^{2}={\tfrac {1}{4}}(4)=1$, so it is true for $n=1$
* Suppose that the statement is true for $k,k\in \mathbb {N}$. That is, suppose that $1^{3}+2^{3}+3^{3}+4^{3}+\cdots +k^{3}={\tfrac {1}{4}}k^{2}(k+1)^{2}$. This is sometimes called the induction hypothesis.
* Then prove the statement for $n=k+1$ (that is, prove that $1^{3}+2^{3}+3^{3}+\cdots +(k+1)^{3}={\tfrac {1}{4}}(k+1)^{2}(k+2)^{2}$:
    ${\begin{aligned}{\mbox{LHS}}&=1^{3}+2^{3}+3^{3}+4+3+\cdots +k^{3}+(k+1)^{3}\\&={\tfrac {1}{4}}k^{2}(k+1)^{2}+(k+1)^{3}&{\mbox{ (by the induction hypothesis)}}\\&={\tfrac {1}{4}}(k+1)^{2}(k^{2}+4(k+1))\\&={\tfrac {1}{4}}(k+1)^{2}(k^{2}+4k+4)\\&={\tfrac {1}{4}}(k+1)^{2}(k+2)^{2}\\&={\mbox{RHS}}\end{aligned}}$
* It follows from parts 1 and 2 by mathematical induction that the statement is true for all positive integers $n$.
# HSC Mathematics Advanced, Extension 1, and Extension 2/3-Unit/HSC/Primitive of sin and cos squared

The integration of these functions can be performed by the substitution of $\sin ^{2}\alpha$ or $\cos ^{2}\alpha$ by a function in terms of $\cos 2\alpha$ respectively.

## Deriving the substituted functions

By the double-angle formula, $\left.\cos 2\alpha =2\cos ^{2}\alpha -1\right.$. Rearranging to make $\cos ^{2}\alpha$ the subject, $\cos ^{2}\alpha ={\tfrac {1}{2}}+{\tfrac {1}{2}}\cos 2\alpha$.
We know by the Pythagorean identity $\left.\sin ^{2}\theta +\cos ^{2}\theta =1\right.$ that $\left.\cos ^{2}\alpha =1-\sin ^{2}\alpha \right.$, so $1-\sin ^{2}\alpha ={\tfrac {1}{2}}+{\tfrac {1}{2}}\cos 2\alpha$. Rearranging, $\sin ^{2}\alpha ={\tfrac {1}{2}}-{\tfrac {1}{2}}\cos 2\alpha$.

## Finding the primitive

By substituting $\sin ^{2}\alpha \,$ for ${\tfrac {1}{2}}-{\tfrac {1}{2}}\cos 2\alpha$, $\int \sin ^{2}\alpha d\alpha =\int {\tfrac {1}{2}}-{\tfrac {1}{2}}\cos 2\alpha d\alpha$. Similarly for $\cos ^{2}\alpha \,$,
$\int \cos ^{2}\alpha \,d\alpha =\int {\tfrac {1}{2}}+{\tfrac {1}{2}}\cos 2\alpha \,d\alpha$
These can be integrated by using the primitives of cosine and sine
$\int \cos \alpha d\alpha =\sin \alpha +c$
$\int \sin \alpha d\alpha =-\cos \alpha +c$
For cos$^2$ α
$\int \cos ^{2}\alpha \,d\alpha =\int {\tfrac {1}{2}}+{\tfrac {1}{2}}\cos 2\alpha \,d\alpha$
$\int {\tfrac {1}{2}}+{\tfrac {1}{2}}\cos 2\alpha \,d\alpha ={\tfrac {1}{2}}\alpha +{\tfrac {1}{4}}\sin 2\alpha +c$
$\int \cos ^{2}\alpha \,d\alpha ={\tfrac {1}{2}}\alpha +{\tfrac {1}{4}}\sin 2\alpha +c$
For sin$^2$ α
$\int \sin ^{2}\alpha \,d\alpha =\int {\tfrac {1}{2}}-{\tfrac {1}{2}}\cos 2\alpha \,d\alpha$
$\int {\tfrac {1}{2}}-{\tfrac {1}{2}}\cos 2\alpha \,d\alpha ={\tfrac {1}{2}}\alpha -{\tfrac {1}{4}}\sin 2\alpha +c$
$\int \sin ^{2}\alpha \,d\alpha ={\tfrac {1}{2}}\alpha -{\tfrac {1}{4}}\sin 2\alpha +c$
# HSC Mathematics Advanced, Extension 1, and Extension 2/3-Unit/Preliminary/Circle geometry

A circle is a 2D shape with no sides, corners or vertices.

# Arc and Angle

Rule 1: Equal arcs subtend equal angles at the centre of the circle.
Rule 2: Equal angles at the centre of the circle subtends equal arcs.
# HSC Physics
## Course Requirements
### Preliminary

The preliminary HSC Physics course consists of four core modules that make up 120 indicative hours in total.
The modules studied are:
* The World Communicates (30 indicative hours);
* Electrical Energy in the Home (30 indicative hours);
* Moving About (30 indicative hours);
* The Cosmic Engine (30 indicative hours).
All four core modules must be completed in order to complete the preliminary physics course. The preliminary physics course is a prerequisite to the HSC physics course.

### HSC

The HSC Physics course consists of three core modules that make up 90 indicative hours in total, and ONE option chosen by the student that makes up 30 indicative hours.
The core modules studied are:
* Space (30 indicative hours);
* Motors and Generators (30 indicative hours);
* From Ideas to Implementation (30 indicative hours).
The options available are:
* Geophysics;
* Medical Physics;
* Astrophysics;
* From Quanta to Quarks;
* The Age of Silicon.
# HSC Physics/Core/From Ideas to Implementation
## Contextual Outline

Text excerpt is from Physics Stage 6 Syllabus
By the beginning of the twentieth century, many of the pieces of the physics puzzle seemed to be falling into place. The wave model of light had successfully explained interference and diffraction, and wavelengths at the extremes of the visible spectrum had been estimated. The invention of a pump that would evacuate tubes to 10$^{−4}$ atmospheres allowed the investigation of cathode rays. X-rays would soon be confirmed as electromagnetic radiation and patterns in the Periodic Table appeared to be nearly complete. The nature of cathode rays was resolved with the measurement of the charge on the electron soon to follow. There was a small number of experimental observations still unexplained but this, apparently complete, understanding of the world of the atom was about to be challenged. The exploration of the atom was well and truly inward bound by this time and, as access to greater amounts of energy became available, the journey of physics moved further and further into the study of subatomic particles. Careful observation, analysis, imagination and creativity throughout the early part of the twentieth century developed a more complete picture of the nature of electromagnetic radiation and matter. The journey taken into the world of the atom has not remained isolated in laboratories. The phenomena discovered by physicists have, with increasing speed, been channelled into technologies, such as computers, to which society has ever-increasing access. These technologies have, in turn, often assisted physicists in their search for further knowledge and understanding of natural phenomena at the sub-atomic level. This module increases students’ understanding of the history, nature and practice of physics and the applications and uses of physics, the implications of physics for society and the environment, and the current issues, research and developments in physics.

## Chapters

* Cathode Rays
* Photoelectric Effect and Black Body Radiation
* Transistors
* Superconductivity
# HSC Physics/Core/From Ideas to Implementation/Cathode Rays
## Introduction

Cathode rays are streams of electrons emitted in a evacuated tube known as a cathode ray tube or a discharge tube. The cathode rays flow from the cathode (negative electrode) to the anode (positive electrode). It is possible to deflect the path of the rays using electric and magnetic fields. This has lead to its use in many applications including the television and the computer.
# Javagony/Other conditions and loops
## Other conditions

We know how to write conditions in Javagony that compare two numbers. What if we want to check for other conditions? Well, this can be done using a Boolean variable, and the function Boolean.compare(b1,true) when b1 is the variable that stores the result of the condition (true or false). It will return 0 if the Boolean variable is true, and -1 if it’s false. She because we already know how to check in Javagony if a number is 0, that means we can check any condition.

## Do/while loop

Now that we know how to check if any condition is true, it’s easy to implement an alternative to a do/while loop in Javagony. All we need to do is to create a function that does something and then calls to itself if the certain condition is met.
For the purpose of this book, we will write a code that prints all powers of 3, until we reach a number that its least significant digit is 7. The last number it will print will be 27.

## While loop

A while loop will work similar to a do/while, only this time we check for the condition at the beginning of the function and not the end. If the condition is met, we execute the code. If it isn’t, we use the return statement to exit from the function. At the end of the function, after executing the code, it will unconditionally call itself.
Let’s use this knowledge to write a code that receives a positive integer, and prints all the digits of the number - starting from the least significant one, and ending with the most significant.
What if we want the function to return the most significant digit? Well, we can easily modify this code to do so.
Let’s modify this code to return an ArrayList that will include all the digits of the number starting from the most significant and ending with the least significant one.
# Javagony/Preface

Javagony (Java + Agony) is an Object-Oriented Esoteric Programming language or a programming challenge using the Java programming language. You can use any Java IDE, but notice that the following statements are NOT allowed:
The purpose of this book is to teach how to write code that does regular Java stuff despite the restrictions.
# Jeep Cherokee
## Maintenance Job How-Tos

* Oil Change
* Radiator Flush and Fill
* Replace wiper-turn signal switch
* Overheating
* 1984 Model Year Cooling System Capacities

## Complete How-Tos

How to set distributor to number one position on a 1986 gm 2.8L Jeep Cherokee.

## Please Edit these How-Tos

* Rear Hatch Won't Open or Won't Close
# Javagony/Conditions: Comparing 2 numbers
## Introduction

As noted in the preface, Javagony does not have if/else statements. However it’s possible to use a try/catch statement instead by putting the code in the try block and causing an error if the condition is met. If an error happens in the try block, the code will move to the catch block. Otherwise, it will continue running in the try block. Therefore we can consider the catch block the if block and the try block (everything that happens after the first line) the else block. Just make sure your code doesn’t generate an error in the try block after the first line, and if you are writing unsafe code (like loading from a file), consider putting a try/catch statement inside the try.
Let’s start with the easiest one, checking if 2 numbers are equal to each other.

## Checking if 2 numbers are equal to each other

As you probably already know by now, if you subtract two numbers that are equal to each other you get zero. Elementary school Mathematics teaches us that it’s impossible to divide a number by zero, and if you try to do so in java it will cause an error. The following code defines 2 variables x and y. If want to you can ask the user to enter them. We will keep thing simple for this example, and their values will be written in the code.

## Comparing 2 integers to check which one is greater

Assume x and y are both integer variables, and that their values have been defined in the program. To check which integer is larger x or y we will use the method Math.addExact(x,Integet.MAX_VALUE-y). The largest number that can be stored in an integer variable is 2,147,483,647. If the result of a normal addition exceeds this value, it will round down. However, if the method Math.addExact is used, it will throw an exception. This behavior can be used to our advantage.
If we want to check if y is greater than x, and not if y is greater or equal to x we can easily swap them in line 10.
# Javagony/External links

* Esolangs wiki entry
* Video by Truttle1
* A blackjack program written in Javagony by Truttle1
* A post about javagony in r/programminghorror
* Javagony algorithms by darenliang
* Brainfuck in Javagony by jammy-dodgers
# Javagony/Common programming problems in Javagony
## Fibonacci numbers

This is a recursive method in Javagony that returns the number in position n of the Fibonacci Sequence.

## Fizz buzz

This is a code in Javagony that prints all the numbers from 1 to 100, but instead of numbers that can be divided by 3, it will print “Fizz”, instead of numbers that can be divided by 5, it will print “Buzz”, and instead of numbers that can be divided by both 3 and 5, it will print “Fizz Buzz”:

## Prime numbers

This is a method in Javagony that gets a number and returns the boolean value true if it’s a prime number. Otherwise, it returns the boolean value false.
# Javagony/Conclusions

In this book, you have learned how to write programs in Javagony that manage to do regular Java tasks despite the limitation of the programming language. Please do not use Javagony for serious projects as it will result in poor performance as well as a messy code. However, you can use Javagony to challenge yourself.
# Jeep Cherokee/1984 Model Year Cooling System Capacities
## 1984 Jeep Cherokee Fluid capacities

This is a list of a fluid capacities of a 1984 Cherokee, broken down by part type

### Coolant Capacity

* 150 cubic inch 4-Cyl.
** Std. 10 quarts/9.5 Liters
** With AC or Heavy Duty Radiator- 10 quarts/9.5 Liters
* 171 cubic inch I6
** Std. 12 quarts/ 11.4 Liters
** With AC or Heavy Duty Radiator- 12 quarts/11.4 Liters

### Oil Capacity

* 150 cubic inch 4-Cyl.
** 4.0 quarts/ 3.8 liters/ 3.3 Imperial quarts
* 171 cubic inch I6
** 4.0 quarts/ 3.8 liters/ 3.3 Imperial quarts

### Transmission Fluid Capacity

* AX4
** 3.5 liters/ 7.4 U.S. pints/ 6.1 Imperial pints of SAE 75W-90 viscosity, GL-5 grade gear lube
* AX5
** 3.3 liters/ 7.0 U.S. pints/ 5.8 Imperial pints of SAE 75W-90 viscosity, GL-5 grade gear lube
* 904 H.D.
** 7.50 Liters/15.8 pints Dexron II ATF

### Transfer Case Fluid Capacity

* Model NP207
** 6 pints/3.82 Liters Dexron II ATF
* Model NP229
** 6 pints/3.82 Liters Dexron II ATF

### Front Differential Fluid Capacity

* Dana 30
** 1.2 Liters/2.5 pints of 75W90 Lubricant

### Rear Differential Fluid Capacity

* Dana 35
** 3 pints/1.41 liters
# High School Earth Science/Earthquakes

* Stress in the Earth's Crust
* Nature of Earthquakes
* Measuring and Predicting Earthquakes
* Staying Safe in Earthquakes
← Theory of Plate Tectonics · Stress in the Earth's Crust →
# High School Earth Science/Ecosystems and Human Populations

* Ecosystems
* The Carbon Cycle
* Human Populations
← Climate Change · Ecosystems →
# High School Earth Science/Erosion and Deposition

* Water Erosion and Deposition
* Wave Erosion and Deposition
* Wind Erosion and Deposition
* Glacial Erosion and Deposition
* Erosion and Deposition by Gravity
← Soils · Water Erosion and Deposition →
# LPI Linux Certification/Install A Boot Manager
## Detailed Objective

(LPIC-1 Version 5.0)
Weight: 2
Description:
Candidates should be able to select, install and configure a boot manager.
Key knowledge area(s):
* Providing alternative boot locations and backup boot options.
* Install and configure a boot loader such as GRUB Legacy.
* Perform basic configuration changes for GRUB 2.
* Interact with the boot loader.
The following is a partial list of the used files, terms and utilities:
* menu.lst, grub.cfg and grub.conf
* grub-install
* grub-mkconfig
* MBR

## Boot managers

A boot loader is installed in the MBR (Master Boot Record). When a system starts, it loads what is in the MBR to RAM. Under Linux there are two main boot loaders:
* Lilo: LInux LOader.
* Grub: GRand Unified Boot Loader.
A boot loader allows you to select the image that you would like to boot from. A system can contain multiple images (operating systems).
A boot loader allows you to interactively run commands and pass parameters to the image that you will boot. The initrd is the driver that will be used to build a filesystem on RAM to mount other filesystems and execute programs.
GRUB is today's default boot loader for many distributions. When installing Windows with Linux, install Windows first and Linux second, because Windows overwrites the MBR without asking.

## LILO vs. GRUB

Both are used to load an image from a disk to RAM. GRUB has the following advantages to LILO:
* More pre-OS commands.
* Supports images stored beyond the 1024 BIOS cylinder limitation.
* Can access its configuration file through the filesystem.
When using LILO, each time you add a new image or change an image a new LILO needs to be installed in the MBR.
* LILO keeps its boot information in the MBR
* GRUB keeps its boot information in the filesystem (menu.lst).
* LILO also has a configuration file /etc/lilo.conf.
To install GRUB on the MBR, use grub-install. The command setup will override the MBR.
To install LILO on the MBR, use lilo. The lilo will use the /etc/lilo.conf file to know what to write into the MBR.
Example of /etc/lilo.conf:
Example of menu.lst (GRUB configuration file):

## Exercises

* Exercises results
1) Install Grub on a floppy disk and try to boot your image manually:
Now reboot with the floppy and from the prompt select the kernel on the hard disk.
2) Create /boot/grub/menu.lst file and install Grub on your hard drive with the grub utility.
3) Install back lilo. Change the linux label of the default kernel image to SuSE in /etc/lilo.conf and re-install the lilo program in the MBR.
# LPI Linux Certification/Implementing Nginx as a web server and a reverse proxy
## Detailed Objectives (208.4)

(LPIC-2 Version 4.5)
Weight: 2
Description: Candidates should be able to install and configure a reverse proxy server, Nginx. Basic configuration of Nginx as a HTTP server is included.
Key Knowledge Areas:
* Nginx
* Reverse Proxy
* Basic Web Server
Terms and Utilities:
* /etc/nginx/
* nginx
# LPI Linux Certification/LDAP Client Usage
## Detailed Objectives (210.3)

(LPIC-2 Version 4.5)
Weight: 2
Description: Candidates should be able to perform queries and updates to an LDAP server. Also included is importing and adding items, as well as adding and managing users.
Key Knowledge Areas:
* LDAP utilities for data management and queries
* Change user passwords
* Querying the LDAP directory
Terms and Utilities:
* ldapsearch
* ldappasswd
* ldapadd
* ldapdelete
# LPI Linux Certification/LDAP Configuration
## Detailed Objectives (210.4)

(LPIC-2 Version 4.5)
Weight: 4
Description: Candidates should be able to configure a basic OpenLDAP server including knowledge of LDIF format and essential access controls.
Key Knowledge Areas:
* OpenLDAP
* Directory based configuration
* Access Control
* Distinguished Names
* Changetype Operations
* Schemas and Whitepages
* Directories
* Object IDs, Attributes and Classes
Terms and Utilities:
* slapd
* slapd-config
* LDIF
* slapadd
* slapcat
* slapindex
* /var/lib/ldap/
* loglevel
# LPI Linux Certification/Install And Configure X11
## Detailed Objectives

(LPIC-1 Version 5.0)
Weight: 2
Description:
Candidates should be able to install and configure X11.
Key Knowledge Areas:
* Understanding of the X11 architecture.
* Basic understanding and knowledge of the X Window configuration file.
* Overwrite specific aspects of Xorg configuration, such as keyboard layout.
* Understand the components of desktop environments, such as display managers and window managers.
* Manage access to the X server and display applications on remote X servers.
* Awareness of Wayland.
The following is a partial list of the used files, terms and utilities:
* /etc/X11/xorg.conf
* /etc/X11/xorg.conf.d/
* ~/.xsession-errors
* xhost
* xauth
* DISPLAY
* X

## Configuration

1. XFree86
type "XFree86 -configure", it will scan your hardware and auto. generate a configuration file matching to your hardware. However, FOR PS/2 MOUSE, you might need to modify this config file manually from ""Device" "/dev/mouse"" to ""Device" "/dev/psaux""
2. Xorg
"Xorg -configure"

### Starting and stopping X

To start X you can use: startx - terminal command used at level 3; edit /etc/inittab to run default at level 5; xinit - when there is no .xinitrc file; init 5 - to change manually runlevel to 5 (and run display manager); xdm - (X Display Manager) - graphical login manager, which run automatically at boot process when starting Linux at level 5 (there are also external graphical login managers ex. kdm, gdm).
To stop X you can use: <CTRL>+<ALT>+<BACKSPACE>; init 3 - at lower level than 5 Linux will stop X-Windows; kill the XFree process.
Configuring X To configure X on a system use XF86Setup. The program will generate a configuration file that will be used by the XFree86 server. To tune the screen under X use Xfine2.
Under X, the user can configure every conceivable aspect of graphic display. Screen font size, styles Pointer behaviour Screen colors Window manager
The tuning can be done on a system-wide or per-user. .xinitrc contains the default window manager and style information to be used by the startx command. This file is usually located under /home/username when defined on a per-user basis. .Xdefaults used to setup pointer behaviour, colors, fonts, etc...

## Exercises

* Exercises results