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For an alternative proof, consider matrix properties. The sum of the diagonal elements of a matrix is called the trace of the matrix. In 2D and 3D every rotation is a planar rotation, and the trace is a function of the angle alone. For a 2D rotation, the trace is 2 cos θ; for a 3D rotation, 1 + 2 cos θ. Examples
Crystallography ranges from the fundamentals of crystal structure to the mathematics of crystal geometry, including those that are not periodic or quasicrystals. At the atomic scale it can involve the use of X-ray diffraction to produce experimental data that the tools of X-ray crystallography can convert into detailed positions of atoms, and ...
A time crystal can be informally defined as a time-periodic self-organizing structure. While an ordinary crystal is periodic (has a repeating structure) in space, a time crystal has a repeating structure in time. A time crystal is periodic in time in the same sense that the pendulum in a pendulum-driven clock is periodic in time.
For example, on the International Space Station the Earth's gravity is nearly 90% as strong as at the surface. Objects orbiting in space would not remain in orbit if not for the gravitational force, and gravitational fields extend even into the depths of intergalactic space. [5] [6] [7] The dark side of the Moon illuminated by the Sun.
[1] [2] The 2005 NASA Authorization Act designated the American segment of the International Space Station as a national laboratory with the goal of increasing the use of the ISS by other federal agencies and the private sector. [3] Research on the ISS improves knowledge about the effects of long-term space exposure on the human body.
Chemical clues in zircon crystals suggest the rock in which they formed came into contact with fresh water 4 billion years ago, when Earth was thought to be covered in ocean.
A vision of a future Moon base that could be produced and maintained using 3D printing [1] Crystals grown by American scientists on the Russian Space Station Mir in 1995: (a) rhombohedral canavalin, (b) creatine kinase, (c) lysozyme, (d) beef catalase, (e) porcine alpha amylase, (f) fungal catalase, (g) myglobin, (h) concanavalin B, (i) thaumatin, (j) apoferritin, (k) satellite tobacco mosaic ...
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