I will give a description of the 2-periodic dg-category of matrix factorizations in terms of "derived algebraic geometry." This description allows one to give geometric meaning to algebraic constructions on the categories, and to give conceptual proofs of the results in the title. If time permits, I'll say something about a useful related viewpoint: matrix factorizations as the Tate construction for a circle action on the dg-category of perfect complexes on the total space.