I need some help understanding mitochondria

[fightclub]

This isn't me trying to get you to do my homework, I'm studying for my next Bio test and my teacher didn't go into mitochondria that much even though she'll be testing us over it soon. Any amount of information at all would be greatly appreciated!

Why does the matrix of the mitochondrial need/have proteins?
& why are the majority of the proteins found in a cell in the mitochondria?

Why & how do ATP synthase in the inner membrane and use the concentration gradient to produce ATP? and what is a concentration gradient?

What is an electron transport chain?

Why is hydrogen released into the matrix of a mitochondria from an electron transport chain?

[JackBean]

Matrix of mitochondria needs proteins for the same stuff as the rest of cell - for catalysis of biochemical reactions.
I doubt that majority of proteins is in mitochondria, it's not like RuBISCO in plant cells.

Concentration gradient is gradient of concentration. If you do not understand to any of these words, look them up. The ATPase uses difference of hydrogen concentrations to synthesise ATP.

C'mon, you really cannot find electron transport chain?

Because the enzymes evolved so. Luckily for us and all living creatures, because otherwise we've had no ETC...