A speed field; It is defined by V(u,v)=(V1/L)(-xi+yj) , here V1 and L are fixed. This...

A speed field; It is defined by V(u,v)=(V1/L)(-xi+yj) , here V1 and L are fixed. This flow is 2 dimensional and stable.

(a)In which position in the flow area does the velocity equal the velocity V1? Make an outline of the speed field by drawing arrows for x>=0 , these arrows should represent fluid velocity in representative positions.

(b)Draw the flow line. (dx/u=dy/v)

Expert Solution

Ally Wells answered 1 year ago

Let A ∈ L(U, V ) and B ∈ L(V, W). Assume that V is finite-dimensional....

Let A ∈ L(U, V ) and B ∈ L(V, W). Assume that V is finite-dimensional. Let X be a 3 × 5 matrix and Y be a 5 × 2 matrix. What are the largest and smallest possible ranks of X, Y, and XY? Give examples of the matrix to support your answers

Let L be a linear map between linear spaces U and V, such that L: U...

Let L be a linear map between linear spaces U and V, such that L: U -> V and let l_{ij} be the matrix associated with L w.r.t bases {u_i} and {v_i}. Show l_{ij} changes w.r.t a change of bases (i.e u_i -> u'_i and v_j -> v'_j)

Let X ∈ L(U, V ) and Y ∈ L(V, W). You may assume that V...

Let X ∈ L(U, V ) and Y ∈ L(V, W). You may assume that V is finite-dimensional. 1)Prove that dim(range Y) ≤ min(dim V, dim W). Explain the corresponding result for matrices in terms of rank 2) If dim(range Y) = dim V, what can you conclude of Y? Give some explanation 3) If dim(range Y) = dim W, what can you conclude of Y? Give some explanation

Let U and V be vector spaces, and let L(V,U) be the set of all linear...

Let U and V be vector spaces, and let L(V,U) be the set of all linear transformations from V to U. Let T_1 and T_2 be in L(V,U),v be in V, and x a real number. Define vector addition in L(V,U) by (T_1+T_2)(v)=T_1(v)+T_2(v) , and define scalar multiplication of linear maps as (xT)(v)=xT(v). Show that under these operations, L(V,U) is a vector space.

An airplane propels itself eastward with speed v. A crosswind with speed u is directed at...

An airplane propels itself eastward with speed v. A crosswind with speed u is directed at an angle θ (0 < θ < π) north of east. What is the distance travelled by the plane after a time t?

let l be the linear transformation from a vector space V where ker(L)=0 if { v1,v2,v3}...

let l be the linear transformation from a vector space V where ker(L)=0 if { v1,v2,v3} are linearly independent vectors on V prove {Lv1,Lv2,Lv3} are linearly independent vectors in V

A fluid flow is defined by u = (0.4x2 + 2t) m/s and v = (0.8x...

A fluid flow is defined by u = (0.4x2 + 2t) m/s and v = (0.8x + 2y) m/s, where x and y are in meters and t is in seconds. Part A Determine the magnitude of the velocity of a particle passing through point x = 12.8 m, y = 1 m if it arrives when t = 3 s. V= Part B Determine the direction of the velocity of a particle passing through point x = 12.8 m,...

The consumption preference function in an economy is defined as: U(c, l) = A ln(c) +...

The consumption preference function in an economy is defined as: U(c, l) = A ln(c) + B ln(l) There is a proportional tax on profits earned by consumers, the consumer's budget constraint function is defined as: c = wN + (1 − τ )π The production function of the firm is defined as: Y = zKαN 1−α 1. What is the consumer's optional budget of consumption and leisure as a function of f w, τ , π, A, B and...

a) Traveling waves propagate with a fixed speed usuallydenoted as v(but sometimes c). The waves are...

a) Traveling waves propagate with a fixed speed usuallydenoted as v(but sometimes c). The waves are called _______________ if their waveformrepeats every time interval T. The fundamental relationship among frequency, wavelength, andvelocity is v=fλ. This relationship may be visualized as follows: In 1 s, f·(1s) cycles of the wave move past an observer. In thissame second the wavetrain moves a distance v·(1s) . c) If the velocity of the wave remains constant, then as thefrequency of the wave is increased,...

Woodstock has preferences for leisure time and birdseed defined by the utility function U(l,B)= l.75B.75, where...

Woodstock has preferences for leisure time and birdseed defined by the utility function U(l,B)= l.75B.75, where l is hours of leisure time and B is the number of birdseeds Woodstock consumes. Suppose Woodstock has 24 hours a day for leisure time and for gathering birdseed. He gathers 20 birdseeds each hour he works (e.g., 20 birdseed is Woodstock’s wage). Let H be the hours Woodstock gathers birdseed. Woodstock chooses leisure time and birdseed according to the optimization problem maxl,b l.75B.75...

Question