In the plane rectangular coordinate system, the coordinates of vertex a of RT △ OAB are (3,1). If △ OAB is rotated 60 ° counterclockwise around point O, and point B reaches point B ', then the coordinates of point B' are______ ．

In the plane rectangular coordinate system, the coordinates of vertex a of RT △ OAB are (3,1). If △ OAB is rotated 60 ° counterclockwise around point O, and point B reaches point B ', then the coordinates of point B' are______ ．

After rotating △ OAB around o point for 60 ° counterclockwise, the position is as shown in the figure. Make B ′ C ′⊥ Y axis at C ′ point, and the coordinates of ∵ a are (3,1), ∵ ob = 3, ab = 1, ∵ AOB = 30 °, ∵ ob ′ = 3, ∵ B ′ OC ′ = 30 °, ∵ B ′ C ′ = 32, OC ′ = 32, ∵ B ′ (32,32)

What is the new function corresponding to the original image of y = x ^ 2 when the plane rectangular coordinate system rotates 45 degrees counterclockwise?

According to the definition of parabola, the distance from the point (x0, Y0) to the focus and the guide line is equal, so: [x0 + (√ 2) /...]

Urgent solution to the initial function problem: square ABCD, side length AB = 4, vertex A and origin coincide
Square ABCD, side length AB = 4, vertex a coincides with the origin, point B is in the first quadrant and ob is 30 ° with the positive direction of X axis, and point D is in the second quadrant
Problem solving guidance
I can't draw the figure. The square is in the first and second image limits, and the lowest vertex A is at the origin O. I don't know how to find the coordinates of point C
"If you can find the BD point, the sum of the coordinates of the two points is the C point, because the midpoint is the same, the sum of the coordinates of the CA point is equal to the sum of the BD points, and the a coordinate is the origin."
How can C be the midpoint of BD? The square is oblique. Can you write it clearly and calculate the result,

You should be able to find out the coordinates of point B. If you can't find out the coordinates of point B, you don't need to look at what I'm talking about below. The coordinates of point B are (double root 3,2). If you set the coordinates of D as x1, y1c as X2, Y2, four unknowns, find four univariate equations, then you can find out equation 1: ab

It is known that the center of square ABCD is at the origin, and the four vertices are on the image of function f (x) = ax ^ 3 + BX (a > 0)
It is known that the center of square ABCD is at the origin, and the four vertices are on the image of function f (x) = ax ^ 3 + BX (a > 0)
If the square ABCD is uniquely determined, try to find the value of B

If the center of ABCD is at the origin, its four vertices must be distributed in four quadrants (including number axis)
Let the coordinates of the vertices of the square in the first quadrant be (m, n), then the coordinates of the vertices in the second, third and fourth quadrants are (- N, m), (- m, - n), (n, - M) respectively
n=am^3+bm -----(1)
m=-an^3-bn ----(2)
(1) × n ^ 3 + (2) × m ^ 3: n ^ 4 + m ^ 4 = BMN ^ 3-bnm ^ 3
Thus, B = (m ^ 4 + n ^ 4) / (Mn ^ 3-nm ^ 3)
Although the final result has not been calculated, then the formula can be solved by applying the basic inequality B = - 2 times the root 2