Differential Geometry | Topology Answers

Find the unit tangent vector at the indicated point of the vector function

r(t)=e^(12t)cost i+e^(12t)sint j+e^(12t) k


T(π/2)=<_,_,_>

Bob claims that he can map Rectangle 1 to Rectangle 2.
Select THREE of the transformations or series of transformations that support his claim.
A
a translation of 2 units down followed by a 180° rotation about the point (1, 2)

B
a reflection over the line x = 0 followed by a reflection over the line y = 4

C
a reflection over the line x = 1 followed by a translation of 2 units down

D
a translation of 12 units right and 2 units down

E
a rotation of 180° about the point (1, 4)

F
a translation of 6 units right

Determine the unit tangent vector at the point (2,4,7) for the circle with parametric equations x=2u, y=u^2 +3 and z=2u^2 +5

The earth is not homogeneous body.It is a dynamic and differentiated body. explain

Define an operator T in End(F^2) by T(x,y)= (y,0) Let

U = {(x,0) | x in F}. Show that

U is invariant under T and T |U is the 0 operator on U;

Prove or disprove any metric defined on X(#0) induces a topology on X

Prove or disprove any metric defined on X(#0) induces a topology on X

Prove or disprove any metric defined on X(#0) induces a topology on X

Prove or disprove every topological space is metrizible