2. Consider the following transformations of R2 Tİ (z, y) (-r, y), T3(x, y) (z, _y), T,(zw) (y, x). Show that, for any j 1,2,3, a subset A C R2 is a Jordan region if and only if T,(A) is a Jordan...
Which of the following transformations T R2 → R is linear? A. T(x,y)=5 OB. T(x,y) = x2 OC. None of the given options OD. TIX.Y)=3x+4y OE. T(x,y) = x2 + y2
2. Given the following three transactions T1 = r1(x); w1(y); T2 = r2(z); r2(y); w2(y); w2(x); T3 = r3(z); w3(x); r3(y); Consider the schedule S = r1(x); r3(z); r2(z); w3(x); r2(y); r3(y); w2(y); w1(y); w2(x); a. Draw the precedence graph of schedule S, and label each edge with data item(s). b. Based on the precedence graph, determine whether S is conflict serializable and justify your answer. If it is serializable, specify all possible equivalent serial schedule(s).
Which of the following are linear transformations? f: R3 R2 [x, y, z] [7x - 2y, 0 h R R x > sin x g R2R [x, y] [y- x, 2 the map T R > R< described by reflection in a line L: 2x + 7y = 0 through the origin.
Consider F and C below. F(x, y, z) = yze?i + e'?j + xyek, C: r(t) - (t? + 1)i + (t? - 1)j + (t– 3t)k, Osts3 (a) pind a function f such that F – Vf. f(x, y, z) (b) Use part (a) to evaluate F. dr along the given curve C.
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C (P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C
Let S be the solid of revolution obtained by revolving the region R of the z y plane about the line z 4where R is the region defined by the curves -6 andy-6- We wish to compute the volume of S by using the method of cylindrical shells a) Determine the smallest x-coordinate 1 and the largest x-coordinate r2 of the points in this region b) Let x be a real number in the interval |1,2 We consider the thin...
The parametric curve r=(2t2+8t−5,−2cos(πt),t3−28t)r=(2t2+8t−5,−2cos(πt),t3−28t) crosses itself at one and only one point. The point is (x,y,z)=(x,y,z)= ( , , ). Let θθ be the acute angle between the two tangent lines to the curve at the crossing point. Then cos(θ)=cos(θ)= (1 point) The parametric curve r (2128t 5,-2 cos(t), 281) crosses itself at one and only one point. The point is (x.y,z- Let 0 be the acute angle between the two tangent lines to the curve at the crossing point....
Consider the following transaction schedule: r1(X), r2(X), r3(X), r1(Y), w2(Z), r3(Y), w3(Z), w1(Y) This schedule is conflict-equivalent to some or all serial schedules. Determine which serial schedules it is conflict-equivalent to, and then identify a true statement from the list below. Select one: a. The schedule is conflict-equivalent to (T3, T1, T2) b. The schedule is not serial c. The schedule is conflict-equivalent to (T3, T2, T1) d. The schedule is conflict-equivalent to (T2, T3, T1) e. The schedule is...
Question 8 (15 marks) Consider the function f: R2 R2 given by 1 (, y)(0,0) f(r,y) (a) Consider the surface z f(x, y). (i Determine the level curves for the surface when z on the same diagram in the r-y plane. 1 and 2, Sketch the level curves (i) Determine the cross-sectional curves of the surface in the r-z plane and in the y- plane. Sketch the two cross-sectional curves (iii) Sketch the surface. (b) For the point (r, y)...
2. [& marks] Consider the line ar transformation T: R – R? T(x,y,z) = (x +y-2, -1-y+z). (a) Show that the matrix [T]s, representing T in the standard bases of Rand R' is of the form [7|6,6= ( +1 -1 1). -1 -1 1 (b) Find a basis of the null space of T and determine the dimension of this space. (c) Find a basis of the range of T and determine the dimension of the range of T. (d)...