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You have a brick of parallelepiped shape. You need to measure its diagonal (a distance between two opposite vertexes remote to the maximum). You have in your disposition a ruler and a rectangular edge of the plane surface (of the table, for example). What should you do to measure the diagonal if
1. You have also a pencil to make marks on the edge of the table.
2. You don't have a pencil but have another identical brick (of the same shape and dimensions).
What is the nullity of the transformation of TsubA? What is the rank of the Transformation TsubA.
Assume that the field is algebraically closed and has zero characteristic, G is finite and representations are finite-dimensional.
Trigonometric function to estimate the exact value.
A recipe uses two eggs, three cups of flour & some other ingredients. The recipe makes enough batter for 6 servings. How many cups of flour will be needed to make enough batter for ten servings?
Explain why vectors QR and RQ are not equivalent. Explain when the elimination method for solving a system of equations is preferable to the substitution method. Give examples.
A firm is faced with the attractive situation in which it can be obtain immediate delivery of item it stocks for retail sale. The firm has, therefore, not bothered to order the item in any systematic way.
With a yearly inflation rate of 7%, prices are given by P=p(1.05)^t, where p is the price in dollars when t=0 and t is the time in years. Suppose p=1. How fast (in cents/ year) are prices rising when t=12?
Prove the proposition. Let X be a metric space and Y be a submetric space of X. If Y is complete, then Y is closed in X. Conversely, if Y is closed in X and X is complete, then Y is complete.
Define a new metric d on X = (0, 1/2)^2 by d((a,b), (r,s)) = 1 if a is not equal to r Or |b - s| if a = r.
Probability: Moment Generating Functions and Poisson Process Let X be a discrete random variable with probability mass function Pr {X=k} = c(1+ k^2) for k= -2, -1, 0, 1, 2.
Using the least squares method answer the following. What are the main strengths of this method?
Given A = a*p_hat + b*psi_hat + c*z_hat (cylindrical unit vectors), where a, b, and c are constants. Is A a constant vector (uniform vector field)? If not, find: the divergence and curl of A
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