OpenLLM-France/wikimedia huggingface dataset:
# Triangle Olive

* Triangle Oak with multiplied columns

## Triangles Olive$_{(Drop)}$

The diagonal of both triangles is Aloe.
🌊    triangle Olive (A227725)    row sums Thyme (A000231) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | sums |
| 0 | 1 · 2 2 | | | | | | 2 |
| 1 | 1 · 2 2 | 1 · 1 1 | | | | | 3 |
| 2 | 1 · 2 2 | 3 · 1 3 | 1 · 2 2 | | | | 7 |
| 3 | 1 · 2 2 | 7 · 1 7 | 7 · 2 14 | 1 · 23 23 | | | 46 |
| 4 | 1 · 2 2 | 15 · 1 15 | 35 · 2 70 | 15 · 23 345 | 1 · 3904 3904 | | 4336 |
| 5 | 1 · 2 2 | 31 · 1 31 | 155 · 2 310 | 155 · 23 3565 | 31 · 3904 121024 | 1 · 134156284 134156284 | 134281216 |
💧    triangle OliveDrop    row sums ThymeDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | sums |
| 0 | 1 · 2 2 | | | | | | 2 |
| 1 | 0 | 1 · 1 1 | | | | | 1 |
| 2 | 0 | 2 · 1 2 | 1 · 2 2 | | | | 4 |
| 3 | 0 | 4 · 1 4 | 6 · 2 12 | 1 · 23 23 | | | 39 |
| 4 | 0 | 8 · 1 8 | 28 · 2 56 | 14 · 23 322 | 1 · 3904 3904 | | 4290 |
| 5 | 0 | 16 · 1 16 | 120 · 2 240 | 140 · 23 3220 | 30 · 3904 117120 | 1 · 134156284 134156284 | 134276880 |
Multiplying the columns with powers of two creates the triangles Poplar$_{(Drop)}$, counting the BF instead of the families.
# Euclidean vector spaces/Injective/Angle-preserving/Inner product formula/Exercise

Let $V$ and $W$ be Euclidean vector spaces, and let
    $\varphi \colon V\longrightarrow W$
denote an injective linear mapping. Show that $\varphi$ is angle-preserving if and only if for all $u,v\in V$, $u,v\neq 0$, the equation
    $\left\langle \varphi (u),\varphi (v)\right\rangle ={\frac {\Vert {\varphi (u)}\Vert }{\Vert {u}\Vert }}\cdot {\frac {\Vert {\varphi (v)}\Vert }{\Vert {v}\Vert }}\cdot \left\langle u,v\right\rangle \,$
holds.
# Circles/Plane/Minimal distance on connecting line/Exercise

Let two disjoint circles $K_{1}$ and $K_{2}$ in the Euclidean plane be given, with centers $M_{1}\neq M_{2}$ and radii $r_{1}$ and $r_{2}$. Show that the distance between the two circles is obtained in points that lie on the connecting line segment of the two centers.
# Skew lines/Distance/2/Exercise

Compute the distance between the two skew lines
    $G={\left\{{\begin{pmatrix}2\\-1\\4\end{pmatrix}}+t{\begin{pmatrix}5\\3\\-2\end{pmatrix}}\mid t\in \mathbb {R} \right\}}\,\,{\text{ and }}\,\,H={\left\{{\begin{pmatrix}4\\-3\\5\end{pmatrix}}+t{\begin{pmatrix}6\\7\\-4\end{pmatrix}}\mid t\in \mathbb {R} \right\}}.$
# Skew lines/Distance/1/Exercise

Compute the distance
    $G={\left\{{\begin{pmatrix}1\\3\\0\end{pmatrix}}+t{\begin{pmatrix}4\\4\\-3\end{pmatrix}}\mid t\in \mathbb {R} \right\}}\,\,{\text{ and }}\,\,H={\left\{{\begin{pmatrix}2\\-6\\3\end{pmatrix}}+t{\begin{pmatrix}5\\7\\2\end{pmatrix}}\mid t\in \mathbb {R} \right\}}.$
# Sequence Heather

~A034343
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 1 | 1 | 2 | 4 | 8 | 16 | 36 | 80 |
Heather appears in the triangles RowanDrop and ElderDrop.
row sums of Lime :
🌊    triangle Elm (A076831)    row sums Clover (A076766) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 2 | 1 | | | | | | 4 |
| 3 | 1 | 3 | 3 | 1 | | | | | 8 |
| 4 | 1 | 4 | 6 | 4 | 1 | | | | 16 |
| 5 | 1 | 5 | 10 | 10 | 5 | 1 | | | 32 |
| 6 | 1 | 6 | 16 | 22 | 16 | 6 | 1 | | 68 |
| 7 | 1 | 7 | 23 | 43 | 43 | 23 | 7 | 1 | 148 |
💧    triangle Lime (~A034253)    row sums Heather (~A034343) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 1 | 1 | | | | | | 2 |
| 3 | 0 | 1 | 2 | 1 | | | | | 4 |
| 4 | 0 | 1 | 3 | 3 | 1 | | | | 8 |
| 5 | 0 | 1 | 4 | 6 | 4 | 1 | | | 16 |
| 6 | 0 | 1 | 6 | 12 | 11 | 5 | 1 | | 36 |
| 7 | 0 | 1 | 7 | 21 | 27 | 17 | 6 | 1 | 80 |
# Sequence Clover

A076766
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 1 | 2 | 4 | 8 | 16 | 32 | 68 | 148 |
The differences with the powers of two are A250003.
MaimedClover is almost Clover − 1. Only the first entry is not reduced.
row sums of Elm :
🌊    triangle Elm (A076831)    row sums Clover (A076766) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 2 | 1 | | | | | | 4 |
| 3 | 1 | 3 | 3 | 1 | | | | | 8 |
| 4 | 1 | 4 | 6 | 4 | 1 | | | | 16 |
| 5 | 1 | 5 | 10 | 10 | 5 | 1 | | | 32 |
| 6 | 1 | 6 | 16 | 22 | 16 | 6 | 1 | | 68 |
| 7 | 1 | 7 | 23 | 43 | 43 | 23 | 7 | 1 | 148 |
💧    triangle Lime (~A034253)    row sums Heather (~A034343) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 1 | 1 | | | | | | 2 |
| 3 | 0 | 1 | 2 | 1 | | | | | 4 |
| 4 | 0 | 1 | 3 | 3 | 1 | | | | 8 |
| 5 | 0 | 1 | 4 | 6 | 4 | 1 | | | 16 |
| 6 | 0 | 1 | 6 | 12 | 11 | 5 | 1 | | 36 |
| 7 | 0 | 1 | 7 | 21 | 27 | 17 | 6 | 1 | 80 |
# Euclidean vector spaces/Angle-preserving/Functorial properties/Exercise

Let $U,V$ and $W$ be Euclidean vector spaces. Show that following statements hold.
a) The identity
    $\operatorname {Id} _{V}\colon V\longrightarrow V$
is angle-preserving.
b) The composition of angle-preserving mappings
    $\varphi \colon U\longrightarrow V$
and
    $\psi \colon V\longrightarrow W$
is again angle-preserving.
c) For a bijective angle-preserving mapping
    $\varphi \colon U\longrightarrow V,$
the inverse mapping is also angle-preserving.
# Euclidean vector space/Angle-preserving/Group/Exercise

Let $V$ be a Euclidean vector space. Show that the set of all angle-preserving mappings
    $\varphi \colon V\longrightarrow V$
is a subgroup of $\operatorname {GL} _{\left(V\right)}$.
# Upper triangular matrix/1/Angle-preserving/Identity/Exercise

Let
    $M={\begin{pmatrix}1&a_{12}&\ldots &\ldots &a_{1n}\\0&1&a_{23}&\ldots &a_{2n}\\\vdots &\ddots &\ddots &\ddots &\vdots \\0&\ldots &0&1&a_{n-1n}\\0&\ldots &\ldots &0&1\end{pmatrix}}\,$
be an upper triangular matrix such that the corresponding linear mapping
    $\varphi \colon \mathbb {R} ^{n}\longrightarrow \mathbb {R} ^{n}$
is angle-preserving, Show
    $M=E_{n}\,.$
# Is big pharma bad?
## Big pharma is bad
### Pro

* Pro It is bad as per Ben Goldacre's book Bad Pharma, 2012 and 2013. See also Wikipedia: Bad Pharma.
* Pro It is bad as per Peter C. Gøtzsche's book Deadly Medicines and Organised Crime, 2013. See also Wikipedia: Deadly Medicines and Organised Crime. See also Google Books preview.
* Pro It is bad as per Gøtzsche 2012, available online.
* Pro It is bad as per Nick Dearden.
* Pro Big pharma systematically broke law in the U.S., resulting in large settlements, per Wikipedia: List of largest pharmaceutical settlements. Not covered is the settlement of Purdue Pharma relating to the U.S. opioid crisis. See also Wikipedia: Purdue Pharma.

### Con

* Con Many products of big pharma save lives and improve health (e.g. antibiotics and insulin) so the big pharma cannot be all bad.
# Diagonal matrix/Angle-preserving/Modulus constant/Exercise

Let
    $M={\begin{pmatrix}d_{11}&0&\cdots &\cdots &0\\0&d_{22}&0&\cdots &0\\\vdots &\ddots &\ddots &\ddots &\vdots \\0&\cdots &0&d_{n-1\,n-1}&0\\0&\cdots &\cdots &0&d_{nn}\end{pmatrix}}\,$
be a diagonal matrix. Show that the corresponding linear mapping
    $\varphi \colon \mathbb {R} ^{n}\longrightarrow \mathbb {R} ^{n}$
is angle-preserving if and only if $\vert {d_{ii}}\vert$ is constant and different from $0$.
# MDLD/angle-preserving (mapping)

Start=angle-preserving (mapping) Target=Linear mapping/Angle-preserving/Definition
# Circles/Distance/1/Exercise

Let $A$ be the circle in $\mathbb {R} ^{2}$ with center $(3,-4)$ and radius $2$, and let $B$ be the circle in $\mathbb {R} ^{2}$ with center $(7,2)$ and radius $3$. Determine the distance between these circle and where this distance is obtained.
# Circle/Line/Distance/1/Exercise

Let $A$ be the circle in $\mathbb {R} ^{2}$ with center $(1,-3)$ and radius $2$, and let $B$ denote the line given by
    $6x+5y=30\,.$
Determine the distance between the circle and the line, and where the distance is obtained.
# Hyperpyramids by a, d, v, g

Analyzing the properties of seals leads to three pairs of number hyperpyramids with axes $^{arity}$/$_{adicity}$, depth, valency and gravity.
overview of the hyperpyramids :
| 🌊 | Wisteria | Syringa (symmetric) | Jacaranda (symmetric) |
| 💧 | WisteriaDrop (symmetric) | SyringaDrop | JacarandaDrop |
overview of the image types :
| adicity 6 | adicity 6 | depth 3 |
by a   (triangles) :
a = 0 :
| | Wisteria | Syringa | Jacaranda |
a = 1 :
| | Wisteria | Syringa | Jacaranda |
a = 2 :
| | Wisteria | Syringa | Jacaranda |
a = 3 :
| | Wisteria | Syringa | Jacaranda |
a = 4 :
| | Wisteria | Syringa | Jacaranda |
a = 5 :
| | Wisteria | Syringa | Jacaranda |
a = 6 :
| | Wisteria | Syringa | Jacaranda |
a = 7 :
| | Wisteria | Syringa | Jacaranda |
by a   (rectangles) :
a = 0 :
| | Wisteria | Syringa | Jacaranda |
a = 1 :
| | Wisteria | Syringa | Jacaranda |
a = 2 :
| | Wisteria | Syringa | Jacaranda |
a = 3 :
| | Wisteria | Syringa | Jacaranda |
a = 4 :
| | Wisteria | Syringa | Jacaranda |
a = 5 :
| | Wisteria | Syringa | Jacaranda |
a = 6 :
| | Wisteria | Syringa | Jacaranda |
a = 7 :
| | Wisteria | Syringa | Jacaranda |
by depth :
depth = 0 :
| | Wisteria | Syringa | Jacaranda |
depth = 1 :
| | Wisteria | Syringa | Jacaranda |
depth = 2 :
| | Wisteria | Syringa | Jacaranda |
depth = 3 :
| | Wisteria | Syringa | Jacaranda |
depth = 4 :
| | Wisteria | Syringa | Jacaranda |
depth = 5 :
| | Wisteria | Syringa | Jacaranda |
depth = 6 :
| | Wisteria | Syringa | Jacaranda |
depth = 7 :
| | Wisteria | Syringa | Jacaranda |
Pair Jacaranda counts seals.  It is a refinement of pyramid pairs Liana (a, d, v) and TwistedLiana (a, d, g), which are refinements of triangle pair Oak (a, d).
Houses have adicity and valency, leading to triangle pair Elm...
Pair Wisteria counts rooms, which are a subdivision of houses.
# R^n/Orthogonal to orthogonal/Not angle-preserving/Exercise

Give, for every $r$, $0\leq r<n$, a linear mapping
    $\varphi \colon \mathbb {R} ^{n}\longrightarrow \mathbb {R} ^{n}$
of rank $r$ with the property that orthogonal vectors are mapped to orthogonal vectors but such that it is not angle-preserving.
# Euclidean vector spaces/Orthogonal to orthogonal/Injective/Angle-preserving/Exercise

Let $V$ and $W$ be Euclidean vector spaces, and let
    $\varphi \colon V\longrightarrow W$
denote an injective linear mapping, fulfilling the property that orthogonal vectors are mapped to orthogonal vector. Show that $\varphi$ is angle-preserving.
# Introduction to Music Theory

Welcome to an Introduction to Music Theory!
This course is designed for students who will be entering careers in music, as well as students who seek to enrich their knowledge of music fundamentals. The purpose of this course is for students to develop skills that will lead to a thorough understanding of music theory and music composition/arranging.
This is the first course in a few courses here on Wikiversity. This particular course is for those students who have very little to no musical experience whatsoever, and simply want to start at the very basics. There are 15 lessons in this particular course along with periodic quizzes, exams, and materials to review.

## Lessons

* What is Music Theory?
* Sound
* The Staff and Clefs
* Rhythm: Notes and Rests
* Meter and Time Signatures
* Notation
* Scales
* Key Signatures and the Circle of Fifths
* Minor Scales: Part I
* Minor Scales: Part II
* Musical Vocabulary
* Other Scales
* Scale Degrees
* Modes
* An Introduction to Singing
# Theory Design Lab

* Science alone of all the subjects contains within itself the lesson of the danger of belief in the infallibility of the greatest teachers in the preceding generation ... Learn from science that you must doubt the experts. As a matter of fact, I can also define science another way: Science is the belief in the ignorance of experts.
—Richard Feynman

## Theory Design Lab

* That which we learn most thoroughly, and remember the best, is what we have in a way taught ourselves.
—On education (Über Pädagogik), Immanuel Kant
The Theory Design Lab is an interdisciplinary facility for the development of virtual theories and resulting simulations and edutainment. Interesting topics for virtual theories include astronomy, exobiology, astrosociobiology, terraforming projects and, of course, Dragon Genetics.
* An experience, a very humble experience, is capable of generating and carrying any amount of theory (or intellectual content), but a theory apart from an experience cannot be definitely grasped even as theory. It tends to become a mere verbal formula, a set of catchwords used to render thinking, or genuine theorizing, unnecessary and impossible. Because of our education we use words, thinking they are ideas, to dispose of questions, the disposal being in reality simply such an obscuring of perception as prevents us from seeing any longer the difficulty.
—Democracy and Education, John Dewey

### Subject "Theory"

Theories from the Theory Design Lab can be used in regular subjects or in a subject "Theory". Theory can have the special property that the teacher presents interdisciplinary topics, possibly following the stated interests and requests of the audience, but that every lesson contains alternative theories, mistakes or describes theories that merely happen to disagree with reality; the audience has to consider the propositions and has to decide which parts they believe in. In theory the audience should vote at the end of each lesson which theories or parts of theories they believe and which parts they don't believe. Theory can have the advantage of edutainment: Some theories may get funny enough to have real entertainment value for a larger audience.

#### Theories

* The more I learn, the more I realize I don't know.
—Albert Einstein
| Predestination Extraterrestrial point of view Conservation law of ideas Xenolinguistics Respect economy Gym class bioethics Colonization of Mars | Observer-psychology effect Theory of thinking Interstellar colonization Defence against the dark arts Prime Directive of the United Federation of Planets |
# ATP tutor course

* Wikiversity
* Assistant teacher program

## Introduction

* Typically, school-based programs focus on addressing students' academic needs; however many such programs actually provide tutoring. One essential difference between tutoring and mentoring is that tutoring is task centered, whereas mentoring can be either relationship centered or instrumental (i.e., goal focused). While a tutor and student may develop a personal bond similar to what characterizes a strong mentoring relationship, this is not essential to the primary goal of tutoring (i.e., academic improvement). Likewise, mentors may engage in activities to improve academics, but the primary goal of these matches is to foster personal bonds between participants.
The ATP tutor course will be an advanced course of the Wikiversity assistant teacher program. The tutor course is not meant as mandatory tuition but should be restricted to high-track students instead. It is not realistic to assume that every pupil can qualify as a tutor.
The goal of the tutor course is to qualify the pupil as an independent tutor for a learning group or course of pupils without need for supervision by a subject teacher. The expectation is that subject teachers will often be present and guide the work of a tutor but that a tutor can be expected to prepare and hold a lesson without the help of a teacher. One could argue that the best practice would be for a tutor only to educate between one and three pupils at the same time but this may commonly be impracticable. The tutor course will encompass self-management training, research training, preparation of materials, didactics and documentation of the work as a tutor. At the end of the course the participants should also be qualified as instructors for the course.
Schools which have no use for tutors can allow tutors to qualify in order to hold voluntary advanced courses, private tutoring courses or extracurricular courses for the school or for the general public.
The tutor course may also become useful for college students without prior experience as tutors.

## Preconditions

Participants should have completed the assistant teacher course or equivalent training and should have gathered some experience as assistant teachers.

## Contents

* Scientific reading and writing skills
# Euclidean vector space/Linear mapping/Angle-preserving/Homothety/Exercise

Let
    $\varphi \colon V\longrightarrow V$
be an angle-preserving linear mapping on the Euclidean vector space $V$. Show that there exists an isometry
    $\psi \colon V\longrightarrow V$
and a homothety
    $\sigma \colon V\longrightarrow V$
such that
    $\varphi =\psi \circ \sigma \,$
holds.
# MDLD/distance (sets)

Start=distance (sets) Target=Metric space/Distance/Subsets/Infimum/Definition
# Point in plane/Line/Distance/Foot/2/Exercise

Determine the distance between the point ${\begin{pmatrix}4\\1\end{pmatrix}}$ and the line given by
    $-6x+3y=11\,.$
Determine also the foot of the perpendicular line of the point to this line.
# Point in plane/Line/Distance/Foot/1/Exercise

Determine the distance between the point ${\begin{pmatrix}5\\-6\end{pmatrix}}$ and the line given by
    $3x-7y=8\,.$
Determine also the foot of the perpendicular line of the point to this line.
# Point in space/Distance to axes spaces/Exercise

Determine the distance between the point ${\begin{pmatrix}7\\-3\\4\end{pmatrix}}$ and each linear subspaces $U_{I}=\langle e_{i},\,i\in I\rangle$ for $I\subseteq \{1,2,3\}$.
# Euclidean vector space/Linear mapping/Angle-preserving/Eigenvalues/Exercise

Let $\varphi \colon V\rightarrow V$ be an angle-preserving linear mapping on the Euclidean vector space $V$. Show that there exists a real number $s$ such that only $s$ or $-s$ might be an eigenvalue of $\varphi$.
# Isometry/Set distances/Exercise

Euclidean vector spaces/Linear mapping/Situation Show that $\varphi$ is an isometry if and only if for arbitrary subsets $A,B\subseteq V$ the equation
    $d(\varphi (A),\varphi (B))=d(A,B)\,$
holds.
# Skew lines/Linear system of equations/2/Exercise

Establish for the skew lines
    $G={\left\{{\begin{pmatrix}5\\3\\-2\end{pmatrix}}+t{\begin{pmatrix}6\\-4\\-1\end{pmatrix}}\mid t\in \mathbb {R} \right\}}\,\,{\text{ and }}\,\,H={\left\{{\begin{pmatrix}-4\\9\\-5\end{pmatrix}}+t{\begin{pmatrix}8\\2\\-6\end{pmatrix}}\mid t\in \mathbb {R} \right\}}$
a linear system of equations, and determine with it the perpendicular line, its feet, and the distance between the two lines.
# Skew lines/Linear system of equations/1/Exercise

Establish for the skew lines
    $G={\left\{{\begin{pmatrix}2\\-5\\6\end{pmatrix}}+t{\begin{pmatrix}7\\-3\\3\end{pmatrix}}\mid t\in \mathbb {R} \right\}}\,\,{\text{ and }}\,\,H={\left\{{\begin{pmatrix}-4\\-4\\-1\end{pmatrix}}+t{\begin{pmatrix}8\\6\\5\end{pmatrix}}\mid t\in \mathbb {R} \right\}}$
a linear system of equations, and determine with it the perpendicular line, its feet, and the distance between the two lines.
# Point in space/Plane/Distance/1/Exercise

Determine the distance between the point ${\begin{pmatrix}3\\-5\\7\end{pmatrix}}$ and the plane given by
    $4x-7y+6z=3\,$
in $\mathbb {R} ^{3}$.
# R^3/Plane by 2x-7y+3z/(4,1,-5)/Distance/Exercise

Determine the minimal distance between $(4,1,-5)$ and a point of the plane $E$ given by the equation $2x-7y+3z=0$.
# Distance/Hyperbola/Union of axes/Exercise

Determine the distance between the hyperbola
    ${\left\{(x,y)\mid xy=1\right\}}$
and the union of axes
    ${\left\{(x,y)\mid xy=0\right\}}.$
# Sequence/Different/Accumulation point/Distance/Exercise

Let ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ be a sequence in a metric space $M$, and suppose that all members are different. Let $A={\left\{x_{n}\mid n\in \mathbb {N} \right\}}$, and let $P$ be a point point from $M$ different from all members. Show that $P$ is a accumulation point of the sequence if and only if
    $d{\left(A,P\right)}=0\,.$
# Standard parabola/Minimal distance to (0,1)/Exercise

For what point $(t,t^{2})$ of the standard parabola becomes the distance to the point $(0,1)$ minimal?
# MDLD/angle-preserving mappings

Start=angle-preserving mappings See=angle-preserving mapping MDLD/angle-preserving mapping Target=Linear mapping/Angle-preserving/Definition
# Cricket

Cricket is an English sport which is very popular in Bangladesh Pakistan, India, Sri Lanka, and many other countries of the world. Cricket is played by two teams and each team comprises of eleven players. There are strict rules and regulations which govern the domestic as well as international cricket. Cricket is playing very important roles in promoting trade and commerce both domestically and internationally. Cricket also serves as a means of diplomacy between various countries. Thus, cricket joins cricketing countries together to promote political ties also.

## Subpages

* Cricket/Players
# Cricket/Players

Here, this page will show all the famous players/current players in each team, that plays Cricket. Clubs most likely won't end up here, just the national team. To see the clubs and it's players, go to Cricket/Clubs and Players to see.

## Australia

* Michael Clarke - Joined the international scene of cricket at age 23. Clarke's batting has reached record breaking levels ever since he took the role as the captain of the Australia National Cricket Team. Only test batsman to reach 4 double centuries in a single, calender year, which was 2012.

## Pakistan

Babar Azam made his international debut at just 16 years old. He once served as a ball boy during a live broadcast Test match and earned praise for his brilliant catch. He made his first-class debut at the age of 16 and his ODI debut for Pakistan at Gaddafi Stadium in Lahore.
# Physics/Pressure

Pressure is defined as force per unit area. Pascal, PSI, bar, atmosphere, kg/square centimeter, etc are the units used for measuring pressure. Pressure is also expressed in mm/cm of Hg or water. 760mm of Hg equals 1 atmosphere, 1 bar, 100000 Pascals, 1 kg/sq. cm or 14.7 PSI(pounds per square inch.
# Guided Tours
### Presentation

| Guided Tours | Introduction | List of Topics | This presentation was made possible by Wikiversal/WikiverSuite, which is made possible by your donation. Thank you for your support. | Introduction |
Guided Tours
a presentation by
Wikiversity Guided Tours
# Linear algebra (Osnabrück 2024-2025)/Symmetries/Cube/Motivation/Example/Examplereferencenumber

Example 49.7