Coordinates of the meter sticks are (0.0) (1,1) (1,0) (0,1) 3 meter sticks form a letter...
3 meter sticks form a letter U. where is the center mass? (xy)
You randomly select a point on a square with corners at (0,0), (0,1), (1,0), (1,1) what os the probability of selecting a poont withon 0.4 of any corner
3. Let S be the triangle with vertices at (0,0), (1,0) and (0,1). Let f (x, y) = e***. Use the change of variables u = x – y, v = x +y to find . f(a,y) dA.
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1), and (1,1). Consider the following integral: 4(x y)e- dA. R Choose a substitution to new coordinates u and v that will simplify this integrand. Draw a sketch of both the region R and the image of the region in the u,v-plane. Evaluate the integral in the new coordinate system. Warning: No matter what strategy you use for this integral, it will require at least...
3. For the equation 24 = r, in 0 <<1,0<t<1, (1,0) = sin(x), on 0 SEST (0,1)=0, u(1. t) = 0, on 0 <t<1, (1) Using the separation of variables, find its solution.
Find the Nash equilibria of the games.
X Y X Y Z 0,4 U 2,0 1,1 3,3 3,3 M 3,4 1,2 2,3 | 0,2 3,0 (b) Y Z 5,1 0,2 U 8,6 8,2 M 0,1 4,6 6,0 M 1,0 2,6 5,1 2,1 3,5 2,8 2,8 0,8 4,4 х 0,0 8,10 4,1 3,10 4,1 B 0,0 3,3 6,4 8,5 6,4 8,5
HW12.2 (3 points) [1,1],[1,0),[1,-1) are the three eigenstates of Lạ& Ly with quantum number l = 1 and m = 1,0,-1, respectively. a) (1 point) What are the following states Lx|1,1) =? Lx|1,0) = ? Lx|1, -1) = ? b) (1 point) Find out eigenstates of Lx that are linear combinations of (1,1),(1,0), and (1,-1) What is the corresponding eigenvalue for each of the eigenstate you find? c) (1 point) What is the matrix representation of Lx in the basis...
4. Stoke's Theorem: Consider a vector field F = (1,1)+(1,0) + (0,0). tyle +rin the unit square bordered by (0,0) + (0,1) ► (a) What is the curl of the vector field F? [2 points) (b) What is the path integral of the vector field around the unit square? [5 points) (c) Show your answers to the previous parts are consistent with Stoke's Theorem. HINT: consider the right-hand rule. (3 points]
7.4 Let X ~ U(-1,1) and Y = x2. a. What are the density, the distribution function, the mean, and the variance of Y: b. What is Pr[Y < 0.5]? 7.5 Let X – U(0,1), and let Y = eax for some a > 0. What are the density, the distribution function, the mean, and the variance of Y?