  We revisit two well-studied scheduling problems in the unrelated machines
setting where each job can have a different processing time on each machine.
For minimizing total weighted completion time we give a 1.45-approximation,
which improves upon the previous 1.488-approximation [Im and Shadloo SODA
2020]. The key technical ingredient in this improvement lies in a new rounding
scheme that gives strong negative correlation with less restrictions. For
minimizing $L_k$-norms of machine loads, inspired by [Kalaitzis et al. SODA
2017], we give better approximation algorithms. In particular we give a $\sqrt
{4/3}$-approximation for the $L_2$-norm which improves upon the former $\sqrt
2$-approximations due to [Azar-Epstein STOC 2005] and [Kumar et al. JACM 2009].
