OpenLLM-France/wikimedia huggingface dataset:
# Space/Plane equation/Example intersection/R/Example

We consider the sets
    $E={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid 5x-y+3z=0\right\}}\,$
(from example) and
    $F={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid 4x+2y-7z=0\right\}}\,,$
and we are interested in the intersection
    $G:=E\cap F={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid 5x-y+3z=0{\text{ and }}4x+2y-7z=0\right\}}\,.$
A point lies in this intersection if and only if it fulfills both conditions, that is, both equations (let us call them $I$ and $II$). Does there exist a "simpler“ description of this intersection set? A point, which fulfills both equations, does also fulfill the equation which arises when we add the equations together, or when we multiply the equation with a number $s\in \mathbb {R}$. Such a linear combination of the equations is, for example,
    $4I-5II=-14y+47z=0\,.$
Therefore
    ${\begin{aligned}G&={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid 5x-y+3z=0{\text{ and }}4x+2y-7z=0\right\}}\\&={\left\{{\begin{pmatrix}x\\y\\z\end{pmatrix}}\in \mathbb {R} ^{3}\mid 5x-y+3z=0{\text{ and }}-14y+47z=0\right\}},\end{aligned}}$
since we can reconstruct the original second equation from the new second equation and vice versa. Hence, the conditions are equivalent. The advantage of the second description is that the variable $x$ does not occur in the new second equation, it has been eliminated. Therefore, we can resolve with respect to $y$ and we obtain
    $y={\frac {47}{14}}z\,.$
For $x$, we must have
    $x={\frac {1}{5}}y-{\frac {3}{5}}z={\frac {1}{5}}\cdot {\frac {47}{14}}z-{\frac {3}{5}}z={\frac {47}{70}}z-{\frac {42}{70}}z={\frac {1}{14}}z\,.$
Also these two resolved equations are together equivalent with the original equations and therefore we have
    $G={\left\{{\begin{pmatrix}{\frac {1}{14}}z\\{\frac {47}{14}}z\\z\end{pmatrix}}\mid z\in \mathbb {R} \right\}}\,.$
This description yields a more explicit overview over the set $G$.
# Space/Cylindrical coordinates/Angle naive/Example

A spatial variant of the polar coordinates are the so-called cylindrical coordinates. A triple $(r,\alpha ,z)\in \mathbb {R} _{+}\times [0,2\pi [\times \mathbb {R}$ is sent to the Cartesian coordinates
    $(x,y,z)=(r\cos \alpha ,r\sin \alpha ,z)\,.$
# Politics and Economics
## Political Economy

Political economy refers to different, but related, approaches to studying economic and political behaviours, ranging from the combining of economics with other fields, to the using of different, fundamental assumptions that challenge orthodox economic assumptions.

## Markets

In orthodox economic theory, there is often much said about the "free" market and pure markets. Orthodox economics advocates a "laissez-faire" approach from government; that the government should intervene as little as possible in the economy, because the market provides the most optimal, efficient outcome. Thus, they regulate de-regulation and privatisation as means to achieve "pure" markets. However, orthodox economics often cannot explain how income gaps around the world are so large, why poverty is still so persistent throughout the world, and the fact that governments still play very important roles in governing the economy. Political Economy looks at the interaction between political and economic forces, which is highly relevant to global issues of the 21st century such as globalisation, international organisations, multi-national corporations, world trade, global governance and international finance, just to name a few.
# Political Sciences in the Ancient Mithila University

<Ancient Mithila University
Political sciences in Mithila is a fascinating subject that explores the history and theory of politics and statecraft in the ancient and medieval region of Mithila, which is now part of Bihar and Nepal. Mithila was known for its rich culture, literature, art, and philosophy, as well as its political institutions and thinkers.
Some of the main aspects of political sciences in Mithila are:
The role of the Janakas, the kings of Mithila, who were also renowned as sages and patrons of learning. They held philosophical dialogues and debates with various scholars and teachers, such as Yajnavalkya, Ashtavakra, Gargi, and Maitreyi. They also established a system of law and justice, and maintained diplomatic relations with other kingdoms.
The development of Nyaya Shastra, the school of logic and epistemology, by Aksapada Gautama, who was born in Mithila. Nyaya Shastra provided the principles and methods of reasoning and argumentation, and was applied to various fields of knowledge, such as ethics, theology, and politics. Nyaya Shastra also influenced the Buddhist and Jain schools of logic.
The contribution of Chandeshvara Thakur, who wrote Rajnītiratnākāra, the oldest work on the subject of state affairs and politics in Mithila, in the second half of the 13th century. He was the most renowned political thinker of Mithila, and was patronized by the Karnata king. Rajnītiratnākāra discussed the topics such as the origin and nature of the state, the qualities and duties of the king, the sources and types of law, the administration and taxation, the foreign policy and war, and the welfare and happiness of the people.
Political sciences of Vidyapati in the Ancient Mithila University is a topic that relates to the life and works of Vidyapati, a famous poet and scholar of Mithila, who lived in the 14th and 15th centuries. Vidyapati was not only a poet of love and devotion, but also a political thinker and advisor, who wrote on various aspects of statecraft, law, diplomacy, and ethics.
# Political Science Construct
## Overview

The Political Science Construct is the conceptualization of how political science is presented on Wikiversity. The Wikiversity School of Political Science builds student knowledge upon four pillars: Political Theory, Government & Politics, Comparative Politics and International Relations. Each of these concepts provides a unique perspective on the study of political science and serves as the core for more advanced and nuanced studies such as the Congress and U.S. Foreign Policy or African E.U. Policy. The -100 level of instruction provides an introduction to these four pillars with an emphasis on the major concepts within the pillar. More detailed instruction in the pillars occurs at the higher course levels. The School does offer a 200 level of instruction which focuses on research, a key takeaway from undergraduate instruction for those students interested in graduate studies. Of note, while graduate studies is not currently offered by the School of Political Science, this course of study will be added to future iterations of the School.

## Political Theory

This is the fundamental pillar of Political Science as it provides the "why?" that describes the "what?", "where?" and "how?" in our course of study. This pillar explores the various political philosophers that have given rise to the field of political science and the intellectual contributions that the philosophers have made that make the subject matter distinct from other schools of study. According to Aristotle "[...] man is a political animal [...]" and thus humanity has developed, distinctive political modalities in the four corners of the planet which allow the study of political theory to be geographically diffuse. In other words, as a student broadens their understanding of the political theories of one side of the planet in addition to the other, their perspective broadens and may change but ultimately provides them with a much more nuanced understanding of global political dimensions.

## Government & Politics

The Government & Politics pillar answers the "what?" question. This a descriptive pillar that seeks to deepen student knowledge about what states, nations and other organizations due to govern and how they politic among themselves. This is an extremely important pillar as it builds our knowledge base of what works and what doesn't work in terms of government and political structures. This pillar explores things like democracy, socialism, and autocracy as well the political parties within a particular political structure such as the political parties of Germany. Individuals that deepen their knowledge in this pillar will be experts in describing political structures for particular countries and organizations such as for Japan or the United Nations. This pillar is partially supported by the theories that may have affected the development of the governmental and political structure in a particular geographic area and serves as a partial support for the study of comparative politics and international relations.
# Poltical science

* Please help develop and classify this resource
* Learn how you can develop this resource to teach participants about Poltical science. Choose a subject, education level, and resource type to classify the resource by. You may learn more about the topic to help you develop and classify the resource from:
Hello. If you know much about political science, please add it here.

## Discussion questions

* What do you see as the biggest political issues facing America? Your country?
* Is democracy the best form of government? What do you see as its strengths and weaknesses?
* In what ways could wikis be used to facilitate the political process?
* What measures should nations take internationally and domestically to encourage environmental sustainability?
* What are the sources of feelings of legitimacy toward a government by a populous? How does the perception of a government as legitimate effect political participation?
Please add more if they come to you.
# Pollution remediation

Part of the Wikiversity Department of Environmental Engineering, School of Engineering and the Engineering and Technology Portal

## Content summary

Remediation of pollution, or clean-up, may require the capture or containment of contaminants.

## Learning Materials
### Texts

* b:IB Biology
* b:Cell Biology
* b:Biochemistry
* b:General Chemistry

### Pollution Remediation Chapters
#### Contaminant Sources
##### Stationary Sources

* Human Waste
* Septic Tanks
* Wastewater Treatment
* Solid Waste (landfills)
* Agricultural Waste
* Green Waste
* Livestock Excrement Piles
* Chemical Byproducts (fertilizers, pesticides)
* Industrial Waste
* Combustion Byproducts
* Leachate from Contaminant Storage
* Offgassing / Volatilization
* Spills

##### Mobile Sources

* Transportation & Shipping
* Livestock
* Wildlife
* Invasive species

#### Contaminant Fate & Transport

* Advection

#### Contaminant Remediation

* Chemical Treatment
* Absorption
* Absorption
* Filtration
* Distillation
* Cement and ImmoCem- waste conversion
* Biological Remediation
* Botanical Uptake - Phytoremediation
* Fungal Uptake - Mycoremediation

## Assignments
### Study guide:

* Wikipedia article:Pollution
* Wikipedia article:Remediation
# Spanish/Verbs/andar/Definition

To walk, amble. From Latin "Ambulare"
# Spanish/Verbs/andar/Present Tense

* Yo ando
* Tú andas
* Él/ella/usted anda
* Nosotros/nosotras andamos
* Vosotros/vosotras andáis
* Ellos/ellas/ustedes andan
# Spanish/Verbs/animar
## A quick note about verbs

* How we regularly talk is in the indicative mood. It is used to state something seen as a fact.
* The subjunctive is a mood used to express desires, doubts, emotions and the unknown. This is NOT a tense! More info about the Subjunctive can be found here.
* The imperative mood is just commands (: It is used to tell someone what to do. For this reason, there is no yo form in the imperative!
* If you don't know which mood to use, just use indicative!
# Spanish/Verbs/bailar/Preterite Tense

Yo bailé- I danced Tú bailaste- You danced Él, ella, usted bailó- He, she, you (polite) danced Nosotros bailamos- We dances Ellos, ellas, ustedes bailaron- They danced
# Spanish/Verbs/bailar
## A quick note about verbs

* How we regularly talk is in the indicative mood. It is used to state something seen as a fact.
* The subjunctive is a mood used to express desires, doubts, emotions and the unknown. This is NOT a tense! More info about the Subjunctive can be found here.
* The imperative mood is just commands (: It is used to tell someone what to do. For this reason, there is no yo form in the imperative!
* If you don't know which mood to use, just use indicative!

## Definition

* to dance -

## Conjugations
### Present Tense (indicative)

Yo bailo- I dance Tú bailas- You dance Él, ella, usted baile- He, she, you (polite) dances Nosotros bailamos- We dance Ellos, ellas, ustedes bailan- They dance

### Preterite Tense (indicative)

Yo bailé- I danced Tú bailaste- You danced Él, ella, usted bailó- He, she, you (polite) danced Nosotros bailamos- We dances Ellos, ellas, ustedes bailaron- They danced
# Spanish/Verbs/bañarse
## A quick note about verbs

* How we regularly talk is in the indicative mood. It is used to state something seen as a fact.
* The subjunctive is a mood used to express desires, doubts, emotions and the unknown. This is NOT a tense! More info about the Subjunctive can be found here.
* The imperative mood is just commands (: It is used to tell someone what to do. For this reason, there is no yo form in the imperative!
* If you don't know which mood to use, just use indicative!
# Spanish/Verbs/bailar/Present Tense

Yo bailo- I dance Tú bailas- You dance Él, ella, usted baile- He, she, you (polite) dances Nosotros bailamos- We dance Ellos, ellas, ustedes bailan- They dance
# Spanish/Verbs/beber
## A quick note about verbs

* How we regularly talk is in the indicative mood. It is used to state something seen as a fact.
* The subjunctive is a mood used to express desires, doubts, emotions and the unknown. This is NOT a tense! More info about the Subjunctive can be found here.
* The imperative mood is just commands (: It is used to tell someone what to do. For this reason, there is no yo form in the imperative!
* If you don't know which mood to use, just use indicative!

## Definition

* to drink -

## Conjugations
### Present Tense (indicative)

Beber in the Present Tense :
| bebo | bebemos |
| bebes | bebéis |
| bebe | beben |

### Preterite Tense (indicative)

Beber in the Preterite Tense :
| bebí | bebimos |
| bebiste | bebisteis |
| bebió | bebieron |

### Imperfect Tense (indicative)

Beber in the Imperfect Tense :
| bebía | bebíamos |
| bebías | bebíais |
| bebía | bebían |

### Conditional Tense (indicative)

Beber in the Conditional Tense :
| bebería | beberíamos |
| beberías | beberíais |
| bebería | beberían |

### Future Tense (indicative)

Beber in the Future Tense :
| beberé | beberemos |
| beberás | beberéis |
| beberá | beberán |

### Present Subjunctive

Beber in the Present Subjunctive :
| beba | bebamos |
| bebas | bebáis |
| beba | beban |

### Past Subjunctive (also called imperfect subjunctive)

Beber in the Past Subjunctive :
| bebiera | bebiéramos |
| bebieras | bebierais |
| bebiera | bebieran |
**Please note: There are two past subjunctive conjugations! The table above depicts the series of endings most widely used today, but below you'll find the other conjugation. The conjugation below is mostly found in older Spanish literature. **
Beber in the Past Subjunctive (option 2) :
| bebiese | bebiésemos |
| bebieses | bebieseis |
| bebiese | bebiesen |
# Spanish/Verbs/beber/Conditional Tense

Beber in the Conditional Tense :
| bebería | beberíamos |
| beberías | beberíais |
| bebería | beberían |
# Q/Archimedes-principle/Dwarfs and giants/Exercise

In the forest, a giant is living, which height is $8$ meter and $37$ cm. There is also a colony of dwarfs, their height at the shoulder is $3$ cm and their height including the head is $4$. The neck and the head of the giant is $1,23$ meter high. On the shoulder of the giant there stands a dwarf. How many dwarfs have to stand above each other (on their shoulders) such that the dwarf on top is at least on the level of the dwarf on the giant?
# QB/AstroJupiter

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863353 for a wikitext version of this quiz.
# QB

Quizbank . Quizbank/QB . Quizbank/QB/d_Conceptual_template . Category:Quizbank/Units . Category:QB/LaTeXpdf . Wright State University Lake Campus
* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
Conceptual Numerical Under discussion Summer 2018 efforts

#### Subpages

Special:Prefixindex/QB/
# QB/AstroApparentRetroMotion

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863420 for a wikitext version of this quiz.
# QB/AstroAtmosphericLoss

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863350 for a wikitext version of this quiz.
# QB/AstroChasingPluto

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863351 for a wikitext version of this quiz.
# QB/AstroGalileanMoons

* Quizbank now resides on MyOpenMath at https://www.myopenmath.com (although I hope Wikiversity can play an important role in helping students and teachers use these questions!)
* At the moment, most of the physics questions have already been transferred. To see them, join myopenmath.com as a student, and "enroll" in one or both of the following courses:
** Quizbank physics 1 (id 60675)
** Quizbank physics 2 (id 61712)
** Quizbank astronomy (id 63705)
The enrollment key for each course is 123. They are all is set to practice mode, giving students unlimited attempts at each question. Instructors can also print out copies of the quiz for classroom use. If you have any problems leave a message at user talk:Guy vandegrift.
* Latest essay: MyOpenMath/Pulling loose threads
* Latest lesson: Phasor algebra
See special:permalink/1863352 for a wikitext version of this quiz.
# Q/b^q/Well-defined/Exercise

Let $b$ be a positive real number and $q=n/m\in \mathbb {Q}$. Show that the number defined by
    $b^{q}:={\left(b^{n}\right)}^{1/m}\,$
is independent of the fraction representation of $q$.
# Preschool Elementary Math/Lesson 3

Template:PreK Elementary Math

## Overview

Students will review numbers 1-10, learn numbers 11-15 and recite them in order. Words you speak are bold, questions you ask are bold and italic and answers to questions are italic. This lesson is in compliance with the 2008 California Preschool Learning Foundations document in section K.NO (Number Sense) in subsection K.1.1 in which students should "Recite numbers in order to twenty with increasing accuracy."

## Lesson Plan

Today we will learn about the numbers 11 through 15, but first we will review numbers 1 through 10. Have them recite the numbers 1 through 10 without your help. Write the number 11 on the board and display 11 objects, drawn on the board or material objects. This is the number 11. Here I have 11 objects. Display another set of 11 objects and ask how many objects it is. Ask them to count with you to find out. Repeat the procedure with the numbers 12 through 15. When this is done, ask who can recite the numbers 1-15. Give a treat or sticker to the child who can complete this task. Then ask them to recite the numbers along with you.

## Homework

Send them home with a page with the numbers 1-15 on it. Instructions for the parent, written on the paper, should ask the parent to recite the numbers with the child and, if possible, reinforce the concept with small objects.

## Next Lesson

The next lesson will be about the numbers 16 through 20.
PreK Elementary Math Lesson 4