I'm reading Flegg's From Geometry to Topology, the author says that in Euclidean geometry, translation and rotation are: $$T:(x,y)\to(x+a,y+b)$$...

I found a Question from the textbook which is not well explained...or not at all explained. And it would be interesting to know how to solve it. Or perhap...

this is a practical problem raised from my chemistry research, apologize if somewhere I used incorrect words. I'm dealing with the derivatives of a v...

While studying graph transformations I came across horizontal and vertical scale and translations of functions. I understand the ideas below. $f(x+a)$ - g...

Derive $\sin{ix}=i\sinh{x}$ from $(5)$. What is $\sin{i}$? $$\cos{x}=\frac{1}{2}\left(e^{ix}+e^{-ix}\right)\quad\text{and}\quad\sin{x}=\frac{1}{2i}\left(e...

What I did. I let $X$ be number of withdraws before $x$ white balls. We can call our succes in this case to be gettin a white ball and probability is of c...

What are autonomous and non-autonomous systems and how are they different from each other. What are the differences between the types of systems they are ...

Cardinality of power set of $A$ is determined by $2^n$, where n is the number of elements in Set $A$. How does this formula work? I was taught that there ...

What is the easiest way to determine that, given 3 coords, they DON'T form a right angled triangle? EG, (0, 0, 0), (0, 1, 0), (1, 0, 0) - forms a rig...

How can I evaluate the derivative $$\left. \frac{d}{dx} \left( x \, \ln(x^5) \right)\right|_{x=1} \, ?$$ I have this math problem, and the biggest thing I...