book Maths Puzzle Numerical Ability

Hi
I have this hw due tomorrow. I really need the solution to this problem ASAP.
Thanks

Question:

let x,y belonging to Rm be fixed vectors. COnsider the
function
f(theta)

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book Other Question

Find a polynomial equation of lowest degree with integer coefficients and has 0, 3, and plus/minus sq rt of 2 as zeros. Please, anyone help. Explain the process and show EACH step in the process of simplifying the following problems:
a. sqrt13 · sqrt5
b. sqrt5 · sqrt7 · sqrt3
c. sqrt3(sqrt3 + sqrt5)