The grammar rule is this: if "who" is the object , then it becomes "whom". In your examples "who" is the object in both cases , so in both cases it should be "whom". You can remember when to use "who/whom" by substituting "he/him" in the sentence . You would not say "With he I am going to the movies"

Both are correct in different ways. The first is the more technically "correct" version, but in reality nobody would say this, unless they were deliberately using artificial-sounding language for a joke. It is a construction that you will only find taught in very outdated textbooks. It sounds extremely unnatural in modern English. The only context where you might hear a question phrased in this way would be a play about upper-class people set in the 1930s! There are two issues here: grammar and appropriacy. The grammar argument is based on two outdated 'rules': 1. "You can't end an utterance with a preposition." This is a piece of nonsense invented by classicists. 2. "You can't use 'who' as the object of a sentence". In reality, we can and we do. The above 'rules' are only obeyed in the most formal of contexts, such as official documents, formal speeches and so on. It is completely inappropriate to attempt to follow these conventions in modern everyday conversations about going to the movies. I would therefore argue that second version is in some ways more correct than the first, given that the first construction is both anachronistic and also inappropriate for the context. "Who are you going to the movies with?" is there only normal way to ask this question in modern English. By the way, you are right that "Whom are you going to the movies with?" is very strange indeed. This is because it is a mixture of two styles/registers - the formal "whom" alongside the neutral-informal word order. We recognise the first construction as something belonging to an earlier era, and we recognise the second as our current way of speaking. Mixing the two really does sound wrong.

"whom" is dying out in British English except among older more Highly educated English speakers. It has become an almost forgotten ancient structure. Sentence two is prefered, unfortunately, it seems to still be taught in classrooms and students spend years trying to work out how to use it. Then when they leave the language courses. To use it, "peer pressure" forces them to adapt to using sentence two.

thanks

ya thats right