I have been sweating over these problems for 4 hours - can someone please help?

Let Z1,...,Zn be identically independently distributed ~N(0,1) random variables. Then what are the distributions and parameters of the following?

1) U=Sigma(n,i=1) Zi ---> I think still just standard normal?

2) V=Sigma(n,i=1) aiZi+bi where ai and bi are real constants --> taking the constant out?

3) W=Sigma(n,i=1) Z^2i ---> chi-squared?

4) Xi=Sigma(n,i=1) cZi+d for all i=1,...,n --> no idea!

Please help, I really have tried by myself!