2. Consider the set of curved coordinates t(t, s) in the plane R2(0,0) related to the Euclidian c...
Consider the set of curved coordinates t := (t, s) in the plane R2V(0,0)} related to the Euclidian coordinates (x, y) by the transformations: s2 +t2 (c) using the formula jar,a-a,aj. Express the vector of first partial derivatives o,0] via a, a, Consider the set of curved coordinates t := (t, s) in the plane R2V(0,0)} related to the Euclidian coordinates (x, y) by the transformations: s2 +t2 (c) using the formula jar,a-a,aj. Express the vector of first partial derivatives...
212 (a) Visualize the vector field on R2\{(0,0)}. More precisely, draw F in the x-y plane by clearly indicating the vector Fr,y) for at least ten points (x,y) in each quadrant. Your drawing should be at scale, following the specifications in the preamble, using clear coordinates and making use of a clearly indicated unit. (b) Find the equations of the flow lines of F, carefully documenting your work out. (c) In a separate diagram, but still following the specifications above,...
The coordinates of a kite in the xy plane are x(t)=At and y(t)=3.0m -Bt2 where a=2.4m/s and B=1.2m/s2. Find vectors v(t), a(t) and magnitudes at 2.0s Possible Answers: ........1: vectors v(t)=A i - 2Bt j, a(t)= -2B j, and magnitude v(2.0s) = -4.8m/s ........2: vectors v(t)=A i - 4Bt j, a(t)= -2B j, and magnitude v(2.0s) = 4.8m/s ........3: None of the above
2. (1 Point) Let r-2u and y-3u. (a) Let R be the rectangle in the uv-plane defined by the points (0,0), (2,0), (2,1), (0 , 1). Find the area of the image of R in the ry plane? (b) Find the area of R by computing the Jacobian of the transformation from uv-space to xy-space Change of Variables When working integrals, it is wise to choose a coordinate system that fits the problem; e.g. polar coordinates are a good choice...
Hi need help for this Question Surface Integral Question: Given Formula Question 2 'Eand G is the surface passing through the points D.E Figure 1 shows 2 curved surfaces. S is the surface passing through the points A, B, Cand D. The equations of both su given in the figure. Determine the unit surface normal for S2 at the poi0,.s a volume directly above S2 and below S 0.5,0.5) and the D1,0,2) S2:z (1-x)(1-y) Figure 1 Equations for curves and...
dx/dt = 4x -x^2 -2xy dy/dt = -y+0.5 xy a) find equilibrium points b) find Jacobian matrix for above system c) find Jacobian matrix at eq. point (0,0) d) draw phase portrait near (0,0) from © e) show at eq. point (4,0) the Jacobian matrix is -4 -8 0 1 f) draw phase portrait near (4,0) from (d) g) at eq. point (2,1) the Jacobian matrix is -2 -4 0.5 0 h) draw phase portrait near (2,1) from (f) i)...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Suppose a plane passes through the points O(0,0,0). B(1,2,2) and C(-1,-1,2) and u -OB and v-OC. (See figure below.) The vector equation of the plane is:x-sutv Choose... s=0, t=0 s-1, t-1 (5,8,2) s--3, t--1.5 (2,5,8) s 3, t-1 s-3, t--2 What values of s and t correspond to point O? What values of s and t correspond to point D? What values of s and t correspond to point B? what values of s and t correspond to point C?...
1 point) Let H be the set of all points in the fourth quadrant in the plane V R2. That is, H- t(x, y) |z 2 0,y S 0. Is H a subspace of the vector space V? 1. Does H contain the zero vector of V? H contains the zero vector of V 2. Is H closed under addition? If it is, enter CLOSED. If it is not, enter two vectors in H whose sum is not in H,...
Question 2 (10 marks) Consider vectors b) (a) Show that B {bi, b2} and Ć = {ci. C2} are bases for R2 (b) Find the B-coordinates of x- (c) Find the change of coordinates matrix Pc-s from B to C and use it to find [x (d) Find the C-coordinates of y - (e) Find the change of coordinates matrix Psc from C to B and use it to find yg Question 2 (10 marks) Consider vectors b) (a) Show...