query: With a two-dimensional, take $(2, 1)$ as the center point and consider a transformation with a rotation angle of $45^\circ$, then point $(3, 3)$
positive_passages.docid: 148716
positive_passages.text: If we take point (2,1) as the center point and ... then point (3, 3) is transformed into point ___
negative_passages.docid: 100404
negative_passages.text: Angle subtended at the centre by a segment of a circle
negative_passages.docid: 28485
negative_passages.text: Commutativity of projection and rotation
negative_passages.docid: 78991
negative_passages.text: How to calculate the rotation matrix between 2 3D triangles?
negative_passages.docid: 79144
negative_passages.text: Prove that the orbit of an iterated rotation of 0 (by (A)(Pi), A irrational) around a circle centered at the origin is dense in the circle.
negative_passages.docid: 131526
negative_passages.text: Prove that the Tangent of 75 degrees equals 2 plus the square-root of 3
negative_passages.docid: 35571
negative_passages.text: Euler Rotations in Ordinary Space
negative_passages.docid: 11338
negative_passages.text: How to find the circumcenter of a triangle and the length of the corresponding radius of the circle in $\mathbb{R}^3$
negative_passages.docid: 79537
negative_passages.text: Finding an unknown linear transformation given that $T(1,1)=(1,0,2)$ and $T(2,3) = (1,-1,4)$
negative_passages.docid: 58000
negative_passages.text: How can one show that a möbius transformation maps the unit circle to some axis?
negative_passages.docid: 16717
negative_passages.text: Possibly rotated parabola from three points
negative_passages.docid: 52857
negative_passages.text: Behaviour of $\frac{x^{3} y}{x^{6} + y^{2}}$ around origin
negative_passages.docid: 87260
negative_passages.text: Let $\theta=\frac{2 \pi}{67}$ consider the rotation matrix $A$. What is $A^{2010}$?
negative_passages.docid: 99384
negative_passages.text: What are the Complex (Non-Real) Eigenvectors of $3\times 3$ Rotation Matrices?
negative_passages.docid: 2064
negative_passages.text: Finite subgroups of orthogonal transformations in $\mathbb{R}^3$
negative_passages.docid: 138596
negative_passages.text: How to get all 24 rotations of a 3-dimensional array?
negative_passages.docid: 14520
negative_passages.text: Get the equation of a circle when given 3 points