On a hot summer day, you need to leave your house for 30 minutes. to use the least amount of energy, should you turn off your air conditioning system, turn up the thermostat, or leave it set at your normal temperature?

Suppose that a comet that was seen in 563 a. d. by chinese astronomers was spotted again in year 1951. assume the time between observations is the period of the comet and take its eccentricity as 0.986. what are (a) the semimajor axis of the comet's orbit and (b) its greatest distance from the sun?

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 ⇒

4. if you were an astronaut on the moon, what would you experience? what would you see from your perspective?