Calculate the flux of the vector field f⃗ =−6i⃗ +5x2j⃗ −5k⃗ , through the square of side 8 in the plane y=1, centered on the y-axis, with sides parallel to the x and z axes, and oriented in the positive y-direction. flux =

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)

Clara is shopping in a grocery store with her friend. each has their own shopping cart in which they want to place their items. the shopping carts are identical. clara and her friend add the same type and number of items to each of their carts. in the baking aisle, however, clara adds 20 pounds of sugar to her own cart, and her friend adds only 10 pounds of sugar to her own cart. which of the following statements best explains what clara must do to accelerate at the same rate as her friend? a. she must add more sugar to her cart. b. she must apply more force to move her cart. c. she must add 20 pounds of salt instead of 20 pounds of sugar to her cart. d. she must apply less force to move her cart.

If you drive 12 miles north and 35 miles east, what is the direct distance between you and your starting point?