Prove that there exists a semi-orthogonal $U$ such that $U^TAU=B$, where $A$ and $B$ are positive-definite symmetric matrices.

Question

Let there be a semi-orthogonal matrix $U \in \mathbb{R}^{m\times n}$ such that $U^TU=I_n$ if $m > n$

If $A \in \mathbb{R}^{m\times m}$ and $B \in \mathbb{R}^{n\times n}$ are positive-definite symmetric matrices,

1. How may I prove that there exists a $U$ such that $$U^TAU=B \quad ?$$

2. Shall we call $U$ a change-of-basis matrix? i.e. changing the bases from dimension $n$ to $m$? OR Is there a better name to describe the transformation done by $U$?

Thanks in advance.