How should I rotate a point $(x,y)$ to location $(a,b)$ on the co-ordinate by any angle?

I have absolutely no clue if any of the terms I used in the title actually exist or make sense. I'm usually good at math (relatively) but I am facing...

What are some particularly well-known functions that exhibit pathological behavior at or near at least one value and are particularly useful as examples? ...

Basically the title, I came across this statement reading some notes on dimension of fibers of flat maps. (I don't know if Noetherian actually matter...

Could someone tell me what the "square of a graph" $G^2$ is? Thanks.

Find all complex numbers $z$ such that $|z| + \overline{z}=9-3i$. Thinking about using with the fact that $z=a+bi$ and $|z| = \sqrt{a^2+b^2}$ in some way....

In many mathematical books that I have read and from lectures from professors, the words 'into' and 'injective' were used interchangea...

There's a proof of that integral on this website: http://math2.org/math/integrals/more/cot.htm I just don't understand why we need the absolute ...

I am quite confused about the meaning of shadow price from explanations on the internet. It can be understood as the value of a change in revenue if the c...

I am having a hard time understanding how a differential equation based on a spring mass damper system $$ m\ddot{x} + b\dot{x} + kx = 0$$ can be described...