Let the matrix representation of the hamiltonian of a three-state system be eo o a h = 0 e 0 la o eo, using the basis states (1), (2), and 3). a) if the state of the system at time t = 0 is v(0)) = 12), what is the probability that the system is in state 2) at time t? b) if, instead, the state of the system at time t = 0 is \v (0)) = 3), what is the probability that the system is in state 3) at time t?

Atank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallons) after t minutes.t(min) 5 10 15 20 25 30v(gal) 694 444 250 111 28 0(a) if p is the point (15, 250) on the graph of v, find the slopes of the secant lines pq when q is the point on the graph with t = 5, 10, 20, 25, and 30.(b) estimate the slope of the tangent line at p by averaging the slopes of two secant lines.(c) use a graph of the function to estimate the slope of the tangent line at p. (this slope represents the rate at which the water is flowing from the tank after 15 minutes.)show all steps.

Sawyer is studying diffraction. he draws a diagram of a plane wave to show how light waves travel. which best describes sawyer’s error? the wave fronts should be perpendicular to the direction in which the waves move. the arrow showing the direction of movement of the waves should be pointing to the left. the arrow showing the direction of movement of the waves should be pointing downward. the wave fronts should be both parallel and perpendicular to the direction in which the waves move.

Explain why you think this diagram shows what happened to the carbon in the biodome.