What is the ruling on swearing by Almighty Allah in a moment of intense anger, and what is the ruling on one who violates his oath after the anger subsides?

If the oath was uttered in a state of anger, without intending to swear an oath, then it falls under 'Laghw al-Yamin' (a vain or unintentional oath) and requires no expiation. However, if you intended the oath and then broke it, you are obligated to offer expiation. This expiation consists of feeding ten poor persons, or clothing them, or freeing a slave. If you cannot find any of these, then you must fast for three days, and it is preferable for them to be consecutive, in accordance with the Almighty's saying: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what you intended of oaths. So its expiation is the feeding of ten poor persons from the average of that which you feed your [own] families, or clothing them, or the freeing of a slave. But he who finds not [the means to do so] - then a fast of three days. That is the expiation for oaths when you have sworn. And guard your oaths. Thus does Allah make clear to you His verses that you may be grateful." [Al-Ma'idah: 89].