f(x,y)=(xcos(t)−ysin(t),xsin(t)+ycos(t))f(x,y)=(xcos⁡(t)−ysin⁡(t),xsin⁡(t)+ycos⁡(t)) defines rotation around the origin through angle tt in the Cartesian plane R2R2. If one...

f(x,y)=(xcos(t)−ysin(t),xsin(t)+ycos(t))f(x,y)=(xcos⁡(t)−ysin⁡(t),xsin⁡(t)+ycos⁡(t))

defines rotation around the origin through angle tt in the Cartesian plane R2R2. If one rotates a point (x,y)∈R2(x,y)∈R2 around the origin through angle tt, then f(x,y)f(x,y) is the result.

Let (a,b)∈R2(a,b)∈R2 be an arbitrary point. Find a formula for the function gg that rotates each point (x,y)(x,y) around the point (a,b)(a,b) through angle tt.

Expert Solution

milcah answered 1 year ago

6) a). Find the equation of the plane through the origin and perpendicular to x+y+z =...

6) a). Find the equation of the plane through the origin and perpendicular to x+y+z = 5 and 2x+y−2z = 7 b). Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5). ( I ) Find an equation for the plane that passes through these three points. ( II ) Find the area of the triangle determined by these three points.

Q.1- At time t=0.00s, a particle located at the origin in the x-y plane has a...

Q.1- At time t=0.00s, a particle located at the origin in the x-y plane has a velocity given by 3.00m/s i + 2.00m/s j. Three seconds later, the velocity is 9.00m/s i - 7.00m/s j. Assume that the particle had a constant acceleration during those three seconds. 1- What was the acceleration of the particle? 2-What is the position of the particle at t=3.00s?

How do you do a 90 degree counter-clockwise rotation around a point? I know around the origin it's (−y,x), but what would it be around a point?

Let T denote the counterclockwise rotation through 60 degrees, followed by reflection in the line y=x...

Let T denote the counterclockwise rotation through 60 degrees, followed by reflection in the line y=x (i) Show that T is a linear transformation. (ii) Write it as a composition of two linear transformations. (iii) Find the standard matrix of T.

Let T denotes the counterclockwise rotation through 60∘, followed by reflection in the line y=x. (i)...

Let T denotes the counterclockwise rotation through 60∘, followed by reflection in the line y=x. (i) Show that T is a linear transformation. (ii) Write it as a composition of two linear transformations. (iii) Find the standard matrix of T.

5. A current loop sits in the x ? y plane, centered on the origin. At...

5. A current loop sits in the x ? y plane, centered on the origin. At the origin, the magnetic field due to the loop points in the positive z direction. What direction does the current in the loop run when viewed from the positive z direction? (a) Counter-clockwise. (b) Clockwise. (c) The current is zero. (d) More information is needed. 6. Two long conducting wires sit parallel to one another. The magnetic field at a point exactly half way...

Three point charges are placed on the x-y plane: a +40.0nC charge at the origin, a...

Three point charges are placed on the x-y plane: a +40.0nC charge at the origin, a -40.0nC charge on the x axis at 10.0cm, and a +100.0nC charge at the point (10.0cm, 9.00cm). (A) Find the total electric force on the +100.0nC charge due to the other two. Please answer in this format: ( ? N)x + ( ? N)y (B) What is the electric field at the location of the +100.0nC charge due to the presence of the other...

Given the plot of y=f(x) below, find the plot of y=f−1(x). A coordinate plane has a...

Given the plot of y=f(x) below, find the plot of y=f−1(x). A coordinate plane has a horizontal x-axis labeled from negative 7 to 7 in increments of 1 and a vertical y-axis labeled from negative 7 to 7 in increments of 1. A curve starts at the point left-parenthesis negative 1 comma 0 right-parenthesis, rises at an increasing rate from left to right and passes through left-parenthesis 1 comma 1 right-parenthesis and left-parenthesis 4 comma 6 right-parenthesis. Select the correct...

The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is...

The plane curve represented by x(t) = t − sin(t), y(t) = 7 − cos(t), is a cycloid. (a) Find the slope of the tangent line to the cycloid for 0 < t < 2π. dy dx (b) Find an equation of the tangent line to the cycloid at t = π 3 (c) Find the length of the cycloid from t = 0 to t = π 2

Convert x=cos(3t)+sin(3t) & y=cos(t)-sin(t) into an equation of x-y form (cartesian equation). Thank you

Question