  We consider here a generalization of the random quantum rotor model in which
each rotor is characterized by an M-component vector spin. We focus entirely on
the case not considered previously, namely when the distribution of exchange
interactions has non-zero mean. Inclusion of non-zero mean permits
ferromagnetic and superconducting phases for M=1 and M=2, respectively. We find
that quite generally, the Landau theory for this system can be recast as a
zero-mean problem in the presence of a magnetic field. Naturally then, we find
that a Gabay-Toulouse line exists for $M>1$ when the distribution of exchange
interactions has non-zero mean. The solution to the saddle point equations is
presented in the vicinity of the bi-critical point characterized by the
intersection of the ferromagnetic (M=1) or superconducting (M=2) phase with the
paramagnetic and spin glass phases. All transitions are observed to be second
order. At zero temperature, we find that the ferromagnetic order parameter is
non-analytic in the parameter that controls the paramagnet/ferromagnet
transition in the absence of disorder. Also for M=1, we find that replica
symmetry breaking is present but vanishes at low temperatures. In addition, at
finite temperature, we find that the qualitative features of the phase diagram,
for M=1, are {\it identical} to what is observed experimentally in the random
magnetic alloy $LiHo_xY_{1-x}F_4$.
