Rotation of Ellipse to FIND the Bxy term, from horizontal to an angle of pi/4

In essence I'm trying to take a horizontal ellipse and put it at an angle, rotating it around the origin. It's for my conics project, I'm making the elliptical orbits of the planets.

So I have the a, b, and c terms of the ellipse, (as in the distance from vertice to center and such) which are 28, 21, and respectively. When plugged into the equation they give:

which turns into

from staring at my math book i've assumed that these x's and y's are actually x prime and y prime in the grand scheme of how we normally look at rotations.

so actually

with this is mind I tried to apply the transformation equations knowing that I was trying to acheive a rotation of

But that's where I get stuck, because I can't think of how to substitute into my prime equation to get ride of the prime variable and create a Bxy term.

So please, its due Wednesday... help?