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This is all down to static electricity.

Inside the Van de Graaff generator, there is a rubber band and rollers. As they are electrically insulated, when the motor turns they rub together ...

Lets say you are in a cubical grain silo, with a height of 12m, and a base with dimensions 3m by 4m. If you wanted to fit a pole in the silo, what is the largest possible length of the pole? 

If we apply a function and then its inverse, we should get back to where we started. 

Suppose we start with an element x. If we apply f to it, we get to x+2. In order to get back to where...

This is often overlooked as no-one gives a reason to why this is and is often stated as a fact. We start off with the basic indice law of x^y * x^z = x^y+z.
For example,...

As often described, a vector is a quantity that has a magnitude and a direction, whereas a scalar just has a magnitude. The easiest way to thing about it is to physically think if you could point in a dir...