For a 2-dimensional (2 eigenvalues / 2 outcomes) problem, the statistical operator can be written as a nice form (20) 1. using the above expression, show that trp 1 which is the standard property of both pure and mixed statistical operators. 2. if |81 1, show that it represents a pure statistical operator.

Arotating space station is said to create “artificial gravity”—a loosely-defined term used for an acceleration that would be crudely similar to gravity. the outer wall of the rotating space station would become a floor for the astronauts, and centripetal acceleration supplied by the floor would allow astronauts to exercise and maintain muscle and bone strength more naturally than in non-rotating space environments. if the space station is 200 m in diameter, what angular velocity would produce an “artificial gravity” of 9.80 m/s^{2} 2 at the rim?

Select all of the following that are equal to an impulse of 20 unitsa) force= 5, time= 5.5b) force= 25, time= 0.8c) force= 0.1, time= 200d) force= 10, time= 2(its b, c, and d)(also in order to find answer they have to add to get the unit)ex= 25x.8=20 or .1x200=20

Avolcano erupts next to a grassland area in a valley. a. describe three ways in which material released by the volcano could impact the grassland area. b. describe three ways in which the grassland ecosystem could recover after a volcanic eruption.