We discussed the properties of operators used in quantum mechanics. let us prove some of the identities mentioned there. 1. show that any linear operator î can be represented as l = a + ib. where a and b are hermitian operators (hint: write a and b in terms of l). (2 pt) 2. consider the commutators (a, bc and ab, ĉof any three linear operators a, b, and ĉ. show that they can be expressed via the commutators (a, b], (a, c), and (b, c). (3 pt) 3. consider the following operator, (a-ib)-1. assuming that is small, expand this operator in a power series in 1. hint: write (a - xb)-1 = "în and determine cn. remember that a and b do not necessar- ily commute

Apulley with a mechanical advantage of 5 will require you to pull times the amount of rope. a. 1/5 b. 5 c. 10 d. 15

Need asap ! what is the relationship between atmospheric pressure and the density of gas particles in an area of increasing pressure? (2 points) as air pressure in an area increases, the density of the gas particles in that area decreases. as air pressure in an area increases, the density of the gas particles in that area increases. as air pressure in an area increases, the density of the gas particles in that area remains constant. as air pressure in an area increases, the density of the gas particles in that area increases and decreases in an alternating pattern. 3. which of the following correctly describes a way in which earth's atmosphere interacts with the geosphere? (2 points) it contains gases that living organisms breathe. it contains gases that trap incoming solar radiation. it provides a medium for cycles that provide nutrients to living organisms. it provides a medium for water to move between earth's surface and the air. 4. which of the following is considered a drawback to using wind energy as a source of power? (2 points) wind energy is nonrenewable. wind energy produces large amounts of air pollution. 5. a meteorologist predicts that the weather in a region will soon change from clear skies to probable thunderstorms. prior to making this prediction, what did the meteorologist most likely observe on a barometer? (2 points) the barometer fell slightly. the barometer fell substantially. the barometer rose slightly. the barometer rose substantially. 6. which of the following do meteorologists not typically use weather balloons to record? (2 points) atmospheric pressure cloud types humidity temperature 7. during which step in the can crush lab did water vapor force air from the can? (2 points) the can was filled nearly to the top with water. the can was placed on the hot stove top burner for several minutes. the can was removed from the hot stove top burner. the can was placed upside-down in the water-filled pan.

Click the game tab at the bottom of the simulation and select level 1. (there is no seesaw balance for this part of the activity.) balance the first equation, and click check to see if you got it right. if you can’t balance it in the first try, you can try again. work through the five equations for level 1. click continue to go on to level 2, and later level 3. each level is more difficult than the one before. keep trying until all the equations are balanced. in one or two sentences, describe how you did in the balancing game. in a few more sentences, explain one strategy you learned for balancing more complex equations.