Many college freshmen describe themselves as pre-med, but a very small percentage of these freshmen will ever attend medical school. After the first course in biology or chemistry, many decide to major in something other than the natural sciences. Which of the twelve principles is at work here?

Why is alternating current more effective at long–distance travel than direct current? a. the power lines are made out of conductors. b. transformers increase or decrease voltage as needed. c. the ac generator is more efficient. d. ac has lower voltage than dc.

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

By what primary heat transfer mechanism does the sun warm the earth?