  The standard-model explanations of the anomalously-large transverse
polarization fraction fT in B -> phi K* can be tested by measuring the
polarizations of the two decays B+ -> rho+ K*0 and B+ -> rho0 K*+. For the
scenario in which the transverse polarizations of both B -> rho K* decays are
predicted to be large, we derive a simple relation between the fT's of these
decays. If this relation is not confirmed experimentally, this would yield an
unambiguous signal for new physics. The new-physics operators which can account
for the discrepancy in B -> pi K decays will also contribute to the
polarization states of B -> rho K*. We compute these contributions and show
that there are only two operators which can simultaneously account for the
present B -> pi K and B -> rho K* data. If the new physics obeys an approximate
U-spin symmetry, the B -> phi K* measurements can also be explained.
