Vector A has a magnitude of 31 units and points in the positive y-direction. When vector B is added to A, the resultant vector A B points in the negative y-direction with a magnitude of 12 units. Find the magnitude and direction of B.

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 ⇒

The energy produced as a result of this flow of electrons from atom to atom is called

Cells in the nervous system have a potential difference of 70 mv across the cell membrane separating the interior of the cell from the extracellular fluid. this potential difference is maintained by ion pumps that move charged ions across the membrane. is this an emf? select the correct answer and explanation. 1)no. the ion pumps cannot separate charges; thus, they cannot create a potential difference. 2)yes. the ion pumps cannot separate charges, but they still can create a potential difference. 3)yes. the ion pumps can actively separate charge; thus, they can create a potential difference. 4)no. the ion pumps can separate charges, but they cannot create a potential difference.