Well, you know that
right? Can you see where to go from here?
If T is "one to one", then it maps the set of basis vectors of U onto an independent set and so maps U onto a subspace of V having exactly the same dimension as U. If not, then it maps U onto a subset of V having smaller dimension. "rank T" is the dimension of T(U).
"rank T" is the dimension of T(U) as above and, of course, T(U) is a subspace of V.rank (T) dim (V)