A sample of matter is at extreme temperatures with particles moving so quickly that their collisions release electrons from the atoms. This creates a mixture of electrons and positively charged ions with high kinetic energy. What phase of matter does this describe?

The phase of matter will be known as the forth phase of matter, plasma.

Explanation:

There are 4 phases of matters:

Gas: The freely moving molecules, having no definite volume and shape. Liquid: The loosely bonded molecules, having a definite volume but not shape. Solid: Highly packed molecules with definite volume and shape. Plasma: The more like gases phase, containing freely moving electrons and positive ions.

Hence according to the question description and given above matter phases, the phase of that sample will be plasma.