Linear transformation from one sample to another
Say we want to sample $x$ from $N(a,b)$. We could certainly do this in R using rnorm(a,b). However, we could also sample $z$ from $N(0,1)$ and apply the linear transformation $a + zb$. This transformation would then give us samples from $N(a,b)$.
What I've described is for the univariate case. You can easily extend this to the multivariate case.