# Tutor profile: Juan V.

## Questions

### Subject: Linear Algebra

If a matrix A is 5 x 3 and the product AB is 5 x 7, what is the size of B?

For the product of AB to be a 5 x 7 matrix, B has to have a size of 3 x 7. Remember when multiplying matrices, that the number of columns of the first matrix in the product must be the same length as the number of rows in the second matrix.

### Subject: Calculus

Find the indicated partial derivative: $R(s,t) = te^{\frac{s}{t}}$; $R_{t}(0,1)$

The subscript t in the condition we are given means we wish to take the partial derivative of R with respect to t at (0,1). Doing so would look like this: $R_{t} = e^{s/t} + \frac{t*-s}{t^{2}}e^{s/t} = e^{s/t} - \frac{s*e^{s/t}}{t}$ $R_{t}(0,1) = e^{0} - 0 = 1 $ So R_{t}(0,1) equals 1.

### Subject: Physics

Consider balancing a hammer upright on the tip of your finger. Would it be easier to balance it with the head of the hammer on your fingertip, or with the handle on your fingertip?

It is easier to balance the hammer with the handle on your fingertip. This is due to the rotational inertia of the hammer (the want for the hammer to rotate) to be greater when most of its' mass distribution is further away from the point of rotation.

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