Draw the vector c⃗ =a⃗ +2b⃗ .
draw the vector c⃗ =1.5a⃗ −3b⃗ .
draw the vector c⃗ =0.5a⃗ +2b⃗ .

Total solidification times of three casting geometries are to be compared: a sphere, a cylinder, in which the length-to-diameter ration - 1.0, and a cube. volume = 1000 cm^3 for all three shhapes, and the same casting alloy is used. a) determine the solidification times of each geometry b) based on the results of part (a), which geometric element would make the best riser? c) if the mold constant = 3.5 min/cm^2 in chvorinov's rule, compute the total solidification time for each casting.

Materials will have different energies associated with the electrons inside them. this is related to how strongly bound they are by their work function. if we sandwich a material with a very low energy between two materials with a high energy, we create a trap for an electron. if this trap is very narrow in one direction in comparison to the others, this is approximately a 1-dimensional box that confines the electron. what is the lowest energy of an electron in the box if the thinnest direction across the materials is 4.81 nm?

The sun's declination is 0° at the a. summer and winter solstice b. summer and winter equinox c. vernal and autumnal solstice d. vernal and autumnal equinox