Just to introduce the background of this question: As many of you know a Rotation Matrix can transform a point $^{B}\textrm{p}$ described in a rotated Coo...

Does anyone have an example of two dependent random variables, that satisfy this relation? $E[f(X)f(Y)]=E[f(X)]E[f(Y)]$ for every function $f(t)$. Thanks....

If $\ 3x^{2}-2x+7=0$ then $$\left(x-\frac{1}{3}\right)^2 =\text{?} $$ I am so confused. It is a self taught algebra book. The answer is: $ \large -\frac{2...

Its very easy to prove $p\mid n^p-n$ for p=3,5,7, it fails for p=9 because $$ (n+1)^9-(n+1)= n^9+9n^8+36n^7+84n^6+126n^5+126n^4+84 n^3+36n^2+8n $$ and $84...

The Generalized Hermitian Gell-Mann Matrices (in dimension $d$ ) consist of the $h_k^d$, where $1\leq k \leq d$, and the $f_{k,j}^d$, where $1\leq k, j\le...

Can anyone help me please. I want to know how to convert a decimal number that has fraction to binary number. For example 1,7 or 24.6 etc... I know how to...

Let $p = (0,0)$ and $q = (1,1)$ be two points. I would like to denote the angle between these two points ($45^\circ)$. I took a look at the lists of symbo...

As you know, $x^2+x+41$ is composite when $x=41$ but, how can I claim that $41$ is the smallest positive integer satisfying condition ? Please explain why

I'm trying to understand why the product of transpositions for a specific permutation is not unique. Intuitively, it somewhat makes sense to me since...

For example the equation $|2x-1|+3=4x$, We can get two equations out of that, $2x-1=4x-3$ and $2x-1=-(4x-3)$. Solve the first one we get $x=1$ and for the...