  We give a rational surgery formula for the Casson-Walker invariant of a
2-component link in $S^{3}$ which is a generalization of Matveev-Polyak's
formula. As application, we give more examples of non-hyperbolic L-space $M$
such that knots in $M$ are determined by their complements. We also apply the
result for the cosmetic crossing conjecture.
