  We consider a population of two-dimensional oscillators with random
couplings, and explore the collective states. The coupling strength between
oscillators is randomly quenched with two values one of which is positive while
the other is negative, and the oscillators can spatially {\it{move}} depending
on the state variables for phase and position. We find that the system shows
the phase transition from the incoherent state to the fully synchronized one at
a proper ratio of the number of positive couplings to the total. The threshold
is numerically measured, and analytically predicted by the linear stability
analysis of the fully synchronized state. It is found that the random couplings
induces the long-term state patterns appearing for constant strength. The
oscillators move to the places where the randomly quenched couplings work as if
annealed. We further observe that the system with mixed randomnesses for
quenched couplings shows the combination of the deformed patterns
understandable with each annealed averages.
