Answer
During the Cenozoic, mammals became more diverse for several reasons: 1) The mass extinction which wiped out the dinosaurs left many niches into which mammals could diversify; 2) Continental drift continued to separate the parts of what had been Pangaea, leaving them in a greater variety of climates, again leaving more niches for mammals to occupy; and 3) Mammals already had adaptations such as greater parental care and endothermy which made them more likely to succeed, to out-compete other animals.
Work Step by Step
The thing to do here is to make a list of mammalian adaptations and to review earlier material on adaptive radiations. Then try to match those features and the events listed in the question with the increased diversity of mammals.
