got trouble selecting prepositions with adjectives

Hi. Many English adjectives can have a prepositional phrase.
My question is that, taking the case of ANGRY,

I'm angry [WITH you] and [AT you]
is both completely equivalent?

I'm angry [AT the delay] and [ABOUT the delay]
also have the same meaning?

If there is any slight difference in meaning, or nuance, between the options, other English adjectives work like that?
for instance,
A. disappointed WITH / IN somebody AT / BY something
B. essential TO /FOR something
C. sorry FOR / ABOUT
and the like
I think there could be some difference in meaning there.

If it really depends on context, I'd be happy if you would tell me examples with the proper situations.

Thanks!