i study alone and i'm having difficulties with these issues, please help me!

Questions:

1- Determine which type of central grid is from its curves. (X ^ 2) / (a ^ 2) + (y ^ 2) / (b ^ 2) - (z ^ 2) / (c ^ 2) = -1

2- Prove that rotations in R ^ 2 commute. Ra * Rb = Rb * Ra

3- Prove that roca in R ^ 3 do not commute.

4- How to transform cylindrical coordinates into Cartesian coordinates?

5- ρ sin ϕ = 2

A surface in R ^ 3 is given by coordinate (ρ, θ, ϕ), how to translate into Cartesian coordinates and what is this surface?

So, the forum is usually happy to help, but will not just give you answers -- just getting answers will not help you learn. What have you tried to do to solve these yourself first? Post the work you've done and the forum will help correct or guide when you get stuck.