OpenLLM-France/wikimedia huggingface dataset:
# Dynamics/Kinematics/Coordinate Systems/Polar
## Introduction

Content from polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuthj. The radial coordinate is often denoted by r or ρ, and the angular coordinate by φ, θ, or t. Angles in polar notation are generally expressed in either degrees or radians (2π rad being equal to 360°).
Polar coordinates are most appropriate in any context where the phenomenon being considered is inherently tied to direction and length from a center point in a plane, such as spirals. Planar physical systems with bodies moving around a central point, or phenomena originating from a central point, are often simpler and more intuitive to model using polar coordinates.
The polar coordinate system is extended to three dimensions in two ways: the cylindrical and spherical coordinate systems.
# Geochronology/Ice cores/Quiz

Ice cores is a lecture from the school of geology.
You are free to take this quiz based on ice cores at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{geology resources}} template. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Tephra layers may be the best geochronometer.
# Geochronology/Mesozoic/Quiz

Mesozoic geochronology is an article and a lecture from the school of geology.
You are free to take this quiz based on Mesozoic geochronology at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{geology resources}} template. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Tephra layers may be the best geochronometer.
# Geochronology/Medieval Warm Period

The Medieval Warm Period (MWP) dates from around 1150 (950 AD) to 750 (1250 AD) b2k.
"A proof-of-concept self-calibrating chronology [based upon the Irish Oak chronology] clearly demonstrates that third order polynomials provide a series of statistical calibration curves that highlight lacunae in the samples."
As indicated in the figures, the data used in the plots comes from radiocarbon dating of Irish Oaks.
Gaps occur near the 720s (1280 b2k), 1070s (930 b2k), 1370s (630 b2k), 1670s (330 b2k), 1800s AD (200 b2k) during the rising Δ$^{14}$C values.
"The number of suitable samples of wood, which connect Antiquity and the Middle Ages is very small [shown in the first figure on the left]. But only a great number of samples would give certainty against error. For the period about 380 AD we have only 3, for the period about 720 AD only 4 suitable samples of wood (Hollstein 1980,11); usually 50 samples serve for dating."
"The center of the graph [in the second image on the left] shows the time axis of conventionally dated historical events. Upper and lower coordinates show reconstructed time tables. The black triangles mark the phantom years."
"In Frankfurt am Main archaeological excavations did not find any layer for the period between 650 and 910 AD."
"Specialists now do not favor the terms “Little Ice Age” and “Medieval Warming Period” since the climatic manifestations of the underlying phenomenon of these [Rapid Climate Change] RCC events can differ greatly from one region of the world to another and the connotations of climate homogeneity within those periods can be misleading."
"When the “Medieval Warming Period” began and ended is defined very differently by scientists and historians, who analyze the diverse data with different methods and chronological smoothing scales and techniques. Furthermore, while historians’ professional background makes them extremely sensitive to chronological precision on the yearly, if not finer, scales, climate scientists often work in thousands, hundreds of thousands, or even millions of years and hence may sometimes seem rather more casual toward a historical time scale."

## Hypotheses

* Each century from 3000 to 500 b2k has been demonstrated to exist by radiocarbon dating or dendrochronology of an artifact.
# Geochronology/Helium dating
## Apatites

Helium dating or (U-Th)/He dating of apatite is also well established from noble gas diffusion studies for use in determining thermal histories, and other, less typical applications such as paleo-wildfire dating.
# Geochronology/Ice cores/Firns

Firn is granular snow, especially on the upper part of a glacier, where it has not yet been compressed into ice.

## Theoretical firn

Def. "a type of old snow which has gone through multiple thaw and refreeze cycles and thus is made of numerous small icy grains, though it is not nearly as saturated with water as snow-cone slush is; can be hard or somewhat soft depending on recent and current weather conditions" is called firn.
Def. "rounded, well-bonded snow that is older than one year; firn has a density greater than 550 kilograms per cubic-meter (35 pounds per cubic-foot); called névé during the first year" is called firn.
# Geochronology/Lichenometry

"Although free-living cyanobacteria are the dominant group in biological crusts covering the inselbergs, the number of cyanobacterial lichens is relatively high and their distribution is homogenous over long distances and macro-climatic gradients."
"Alectorioid lichens are the dominant group of epiphytic lichens in boreal forests."
"The dominant group of lichens in tropical rain forests are crustose microlichens, a highly diverse assemblage that lacks detailed taxonomic and ecological studies, among them the families Graphidaceae and Thelotremataceae (Wirth and Hale 1963, 1978; Hale 1974, 1978"
# Determinant function/Uniquely determined/Fact

Let $K$ be a field and $n\in \mathbb {N}$.
determinant function
    $\triangle \colon \operatorname {Mat} _{n}(K)=(K^{n})^{n}\longrightarrow K$
fulfilling
    $\triangle {\left(e_{1},\,e_{2},\ldots ,e_{n}\right)}=1\,,$
where $e_{i}$ denote the standard vectors, namely the
# Determinant problem

Problem: Given a square, $m\times m$ matrix $M$ whose diagonal elements are each equal to $m$ and whose non-diagonal elements are each equal to $-1$, calculate its determinant.
In symbols,
    $\Delta ={\begin{vmatrix}m&-1&-1&\dots &-1\\-1&m&-1&\dots &-1\\-1&-1&m&\dots &-1\\\vdots &\vdots &\vdots &\ddots &\vdots \\-1&-1&-1&\dots &m\end{vmatrix}}$
What is $\Delta$ as a function of $m$?
Solution.
# Determinant function/Definition

Let $V$ be a vector space over a field $K$ of dimension $n$. A mapping
    $\triangle \colon V^{n}\longrightarrow K$
is called a determinant function if the following two conditions are fulfilled.
* $\triangle$ is multilinear.
* $\triangle$ is alternating.
# Deterrence

part of the School of Strategic Studies
Deterrence, in military terms, is the dissuasion of hostile activity by working to make such activity appear unprofitable. This can be obtained by threatening the adversary either to suffer prohibitive costs if he tries to achieve his aims by force (deterrence "by punishment") or to deny him the ability to do so (deterrence "by denial").
The term is most often used since the Second World War in regards to nuclear weaponry, but deterrence as such may also be obtained by other weapons of mass destruction (biological or chemical weapons) or by armies organized for waging conventional war. That is why, following Patrick Morgan (1977, 2003), some scholars have made a distinction between "general deterrence", which rests on dissuading any potential agressor by implicit threats, and "immediate deterrence", backed by explicit conventional and/or nuclear threats.
The chief idea of deterrence by the threat of punishment is to guarantee that, in the event of an engagement in which nuclear devices are employed, the aggressor would be as thoroughly devastated as the conquered party.
# Determinant function/Behavior under row operations/Fact/Proof

(1) and (2) follow directly from multilinearity. (3) follows from fact. To prove (4), we consider the situation where we add to the $s$-th row the $a$-multiple of the $r$-th row, $r<s$. Due to the parts already proven, we have
    $\triangle {\begin{pmatrix}\vdots \\v_{r}\\\vdots \\v_{s}+av_{r}\\\vdots \end{pmatrix}}=\triangle {\begin{pmatrix}\vdots \\v_{r}\\\vdots \\v_{s}\\\vdots \end{pmatrix}}+\triangle {\begin{pmatrix}\vdots \\v_{r}\\\vdots \\av_{r}\\\vdots \end{pmatrix}}=\triangle {\begin{pmatrix}\vdots \\v_{r}\\\vdots \\v_{s}\\\vdots \end{pmatrix}}+a\triangle {\begin{pmatrix}\vdots \\v_{r}\\\vdots \\v_{r}\\\vdots \end{pmatrix}}=\triangle {\begin{pmatrix}\vdots \\v_{r}\\\vdots \\v_{s}\\\vdots \end{pmatrix}}\,.$
(5). If a diagonal element is $0$, then set $r=\max {\left\{i\mid a_{ii}=0\right\}}$. We can add to the $r$-th row suitable multiples of the $i$-th rows, $i>r$, in order to achieve that the new $r$-th row is a zero row, without changing the value of the determinant function. Due to (2), this value is $0$.
In case no diagonal element is $0$, we may obtain, by several scalings, that all diagonal element are $1$. By adding rows, we obtain furthermore the identity matrix. Therefore,
    $\triangle (M)=a_{11}a_{22}\cdots a_{nn}\triangle (E_{n})=a_{11}a_{22}\cdots a_{nn}\,.$
# Determining and confirming client business expectations and needs

From the official document:
    "This unit defines the competency required to determine client business requirements and verify the accuracy of the information gathered."
Basically, that means asking good questions, listening well and checking the answers. Sometimes it can mean doing a little educating too - some clients don't know what's possible until you tell them.
You can read more about this unit on the National Training Information Systems Official document for ICAA4041A.
This unit forms part of the following qualifications:
* Cert IV Websites Qualification in Australia
* Cert III Applications Qualification in Australia

## How this unit will help you

After learning and applying the skills required by this unit you'll be able to demonstrate your skills in:
* Defining and documenting problems
* Gathering information
* Getting sign-off from your client

## Ideas for learning the required skills

Pick up a copy of - A Guide to Understanding and Diagnosing Our Clients’ Business – The Fallon Way and work through it for a business in your area. Although written by an advertising agency for campaign creation, there are a number of similarities to web site design.

## Ideas for demonstrating this unit

The best way to demonstrate these skills is ...

## Grading

If you are demonstrating this unit as part of a formal course, you might find that the unit is graded (meaning you can not only demonstrate your competence, but can also gain a credit or distinction). Your facilitator may already have set criteria that your college uses. If not, here are some ideas for possible credit/distinction activities that you can discuss with your facilitator:
# Gases/Gaseous objects/Astronomy/Quiz

Gaseous-object astronomy is a lecture about specific astronomical entities composed mostly of gases at least as detected. It is also a lecture as part of the radiation astronomy series on object astronomy.
You are free to take this quiz based on gaseous-object astronomy at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{radiation astronomy resources}} template. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Gaseous objects in the interplanetary medium have their shapes affected by the solar wind.
# Gases/Gaseous objects/Quiz

Gaseous objects is a lecture about specific astronomical, chemical, and physical entities composed mostly of gases at least as detected. It is also a lecture as part of the radiation astronomy department series on object astronomy.
You are free to take this quiz based on gaseous objects at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{radiation astronomy resources}}, {{chemistry resources}}, and {{physics resources}} templates. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Gaseous objects in the interplanetary medium have their shapes affected by the solar wind.
# Gases/Gaseous objects/Earth/Quiz

Earth as a gaseous object is a lecture about a specific astronomical, chemical, and physical entity composed mostly of gases at least as detected. It is also a lecture as part of the radiation astronomy department series on object astronomy.
You are free to take this quiz based on Earth as a gaseous object at any time.
To improve your score, read and study the lecture, the links contained within, listed under See also, External links, and in the {{radiation astronomy resources}}, {{chemistry resources}}, and {{physics resources}} templates. This should give you adequate background to get 100 %.
As a "learning by doing" resource, this quiz helps you to assess your knowledge and understanding of the information, and it is a quiz you may take over and over as a learning resource to improve your knowledge, understanding, test-taking skills, and your score.
Suggestion: Have the lecture available in a separate window.
To master the information and use only your memory while taking the quiz, try rewriting the information from more familiar points of view, or be creative with association.
Enjoy learning by doing!

## Hypotheses

* Gaseous objects in the interplanetary medium have their shapes affected by the solar wind.
# Engineering Projects/Poppit/Howard Community College/Fall2011/502 TDM/502 Dkirby7518/Poppit/Howard Community College/Fall2011
## Electronic Sections Expected
### Problem Statement

Put the last negotiated problem statement with the instructor or client of the project here.

### Team Members

Put each team members name here with links to their personal page here. Real names do not have to be used.

### Summary

Put an overall, one paragraph summary here with links to the team weekly reports.

### Poster

Put a graphic in wikimedia, include the graphic here or link to it here. The graphic should be suitable for creating a traditional project poster.

### Story

Tell a story of the project. Describe how split up, what the obstacles were, what testing was done, what informal decisions were made, what assumptions were made, what the results were. This is a longer version of the summary with links to all the details collected associated with the project. These links could be to software, links to videos, links to project pages with pictures, etc. Think of the story as a summary of the team weekly reports on one long page rather than a short paragraph like the summary.

### Decision List

List all formal decisions made with links to their documentation such as a decision tree or decision matrix.

### Material List

Figuring out what to purchase, what to build, what everything costs is a huge part of engineering. Typically there is a list of materials in stock, materials that are ordered, materials that should be ordered next time there is money, materials that have not been fully justified. These issues are part of healthy management of the engineering lab but are associated with a particular college. The detail needs to be published in this "Done" form. However in the project root, just a list of materials is necessary.

### Software List

Installing and learning different software packages is part of most engineering project just like the materials list.

### Time

Time estimates and actual time consumed measurements helps justify salaries (grades). The only way to gain respect for estimated project time and costs is to practice.

### Tutorials

Most projects consist of making instructions to jump start the next team, shrink the learning of tools and software to the minimum, advice on where to purchase materials, how to assemble, etc. Tutorials modified or created are described here with links.

### Next Steps

If this is not filled out, the next team may have to repeat each of your steps just to figure out what the next step is. It is best to write this immediately at the end of the project while creating the summary, poster, presentation, and story.
# Engineering Projects/Poppit/Howard Community College/Fall2011/502 TDM/502 Mscobell1809/Poppit/Howard Community College/Fall2011/502 TDM
## Electronic Sections Expected
### Problem Statement

Put the last negotiated problem statement with the instructor or client of the project here.

### Team Members

Put each team members name here with links to their personal page here. Real names do not have to be used.

### Summary

Put an overall, one paragraph summary here with links to the team weekly reports.

### Poster

Put a graphic in wikimedia, include the graphic here or link to it here. The graphic should be suitable for creating a traditional project poster.

### Story

Tell a story of the project. Describe how split up, what the obstacles were, what testing was done, what informal decisions were made, what assumptions were made, what the results were. This is a longer version of the summary with links to all the details collected associated with the project. These links could be to software, links to videos, links to project pages with pictures, etc. Think of the story as a summary of the team weekly reports on one long page rather than a short paragraph like the summary.

### Decision List

List all formal decisions made with links to their documentation such as a decision tree or decision matrix.

### Material List

Figuring out what to purchase, what to build, what everything costs is a huge part of engineering. Typically there is a list of materials in stock, materials that are ordered, materials that should be ordered next time there is money, materials that have not been fully justified. These issues are part of healthy management of the engineering lab but are associated with a particular college. The detail needs to be published in this "Done" form. However in the project root, just a list of materials is necessary.

### Software List

Installing and learning different software packages is part of most engineering project just like the materials list.

### Time

Time estimates and actual time consumed measurements helps justify salaries (grades). The only way to gain respect for estimated project time and costs is to practice.

### Tutorials

Most projects consist of making instructions to jump start the next team, shrink the learning of tools and software to the minimum, advice on where to purchase materials, how to assemble, etc. Tutorials modified or created are described here with links.

### Next Steps

If this is not filled out, the next team may have to repeat each of your steps just to figure out what the next step is. It is best to write this immediately at the end of the project while creating the summary, poster, presentation, and story.
# Engineering Projects/Poppit/Howard Community College/Fall2011/502 1+2=11
### Problem Statement

Put the last negotiated problem statement with the instructor or client of the project here.

### Team Members

Dominick Moreno
Wesley Rodriguez
Dominick Moreno

### Summary

Put an overall, one paragraph summary here with links to the team weekly reports.

### Poster

Put a graphic in wikimedia, include the graphic here or link to it here. The graphic should be suitable for creating a traditional project poster.

### Story

Tell a story of the project. Describe how split up, what the obstacles were, what testing was done, what informal decisions were made, what assumptions were made, what the results were. This is a longer version of the summary with links to all the details collected associated with the project. These links could be to software, links to videos, links to project pages with pictures, etc. Think of the story as a summary of the team weekly reports on one long page rather than a short paragraph like the summary.

### Decision List

List all formal decisions made with links to their documentation such as a decision tree or decision matrix.

### Material List

Figuring out what to purchase, what to build, what everything costs is a huge part of engineering. Typically there is a list of materials in stock, materials that are ordered, materials that should be ordered next time there is money, materials that have not been fully justified. These issues are part of healthy management of the engineering lab but are associated with a particular college. The detail needs to be published in this "Done" form. However in the project root, just a list of materials is necessary.

### Software List

Installing and learning different software packages is part of most engineering project just like the materials list.

### Time

Time estimates and actual time consumed measurements helps justify salaries (grades). The only way to gain respect for estimated project time and costs is to practice.

### Tutorials

Most projects consist of making instructions to jump start the next team, shrink the learning of tools and software to the minimum, advice on where to purchase materials, how to assemble, etc. Tutorials modified or created are described here with links.

### Next Steps

If this is not filled out, the next team may have to repeat each of your steps just to figure out what the next step is. It is best to write this immediately at the end of the project while creating the summary, poster, presentation, and story.