Hello, magentarita!

I'll walk through the first one . . .

Given the general quadratic: .Determine the appropriate rotation formulas to use

so that the new equation contains no -term.

. . the angle of rotation is given by: .

. . and the new coordinates are: .

We have: .

. . Then: .

. . Hence: .

And we have: .

Substitute into: .

. .

. .

. .

. .

. .