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The group SO(3) can therefore be identified with the group of these matrices under matrix multiplication. These matrices are known as "special orthogonal matrices", explaining the notation SO(3). The group SO(3) is used to describe the possible rotational symmetries of an object, as well as the possible orientations of an object in space.
The universal cover of SO(3) is a Lie group called Spin(3). The group Spin(3) is isomorphic to the special unitary group SU(2); it is also diffeomorphic to the unit 3-sphere S 3 and can be understood as the group of unit quaternions (i.e. those with absolute value 1).
The compound is prepared by treating V 2 O 5 in sulfuric acid with elemental sulfur: [2] V 2 O 5 + S + 3 H 2 SO 4 → V 2 (SO 4) 3 + SO 2 + 3 H 2 O. This transformation is a rare example of a reduction by elemental sulfur. When heated in vacuum at or slightly below 410 °C, it decomposes into vanadyl sulfate (VOSO 4) and SO 2. Vanadium(III ...
H 2 S 2 O 5 +5 (of the sulfur atom bonded to 3 oxygen atoms), +3 (of other sulfur atom) Disulfite commonly known as metabisulfite, S 2 O 2− 5: Not known. Sulfurous acid: H 2 SO 3 +4 Bisulfite, HSO − 3 and sulfite, SO 2− 3: Not known. Dithionous acid: H 2 S 2 O 4 +3 Dithionite, O 2 SSO 2− 2: Not known. Sulfoxylic acid: H 2 SO 2 +2 ...
Sulfuric(IV) acid (United Kingdom spelling: sulphuric(IV) acid), also known as sulfurous (UK: sulphurous) acid and thionic acid, [citation needed] is the chemical compound with the formula H 2 SO 3. Raman spectra of solutions of sulfur dioxide in water show only signals due to the SO 2 molecule and the bisulfite ion, HSO − 3 . [ 2 ]
XO-3 is a star in the constellation Camelopardalis. The star has a magnitude of 10 and is not visible to the naked eye but is visible through a small telescope . [ 3 ] A search for a binary companion star using adaptive optics at the MMT Observatory was negative.
Most frequently made from a single piece of bamboo, the sáo measures between 40 and 55 centimeters in length and 1.5 to 2 centimeters in diameter, with six or ten finger holes and a tuning slide. [1] [2] Located inside the bamboo tube, near the oval blowing hole, is a soft wooden piece that adjust pitches when necessary. The first hole after ...
The XO's own action station is in a separate part of the ship from that of the captain, so that a single hit will not likely incapacitate both officers. [1] On small ships with no first lieutenant , gunnery officer , or navigator , the executive officer may also be responsible for the duties of those officers. [ 2 ]