Multipole Expansion Homework: Invariance w/ Orthogonal Rotation

[xlotox]

Homework Statement

Given the multipole moment of the mass distribution how would I go about determining that the multipole moment expansion is invariant. I

Homework Equations

http://cohengroup.ccmr.cornell.edu/courses/phys3327/HW2/hw2.pdf

The Attempt at a Solution

I need to explicitly show how the coordinates transform over an orthogonal rotation. I'm not sure how to do this part explicitly and for an expansion of any multipole term. The link to EX 2.2 is similar to what I'm asking but instead of a translation I need to show for a rotation of the basis.

 

[Nate810]

I think this is done by showing how the coordinates transform under a rotation in the xy-plane. I'm not sure how to go about doing this for an arbitrary multipole moment.