on the other hand = however; but. Used for showing contrast

Visiting China for the Olympics this year would be fun; on the other hand, it might be really expensive. We should wait until next year.

on the dot = exactly on time

Ms. Johnson expects her employees to arrive at work every morning on the dot–or earlier.

once again = another time; once more.

Once again, he’s hurt his back by trying to lift something heavy. His wife keeps telling him not to even try.

open to = ready to accept new ideas.

It’s a wise person who is open to new ideas.

Are you open to learning new things?