In linguistics, diaeresis, diæresis or dieresis, is the pronunciation of two adjacent vowels in two separate syllables rather than as a diphthong or vowel digraph, and also the name of the diacritic mark ( ¨ ) used to prompt the reader to pronounce adjacent vowels in this manner. For example the first two vowels in the word cooperate, which can be spelt co-operate or, using the diaeresis, coöperate.
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It depends on the language. In most languages, it's to indicate that the a should NOT be combined with the adjacent vowel, but pronounced in a separate syllable. In German, however, it changes the sound of the vowel itself. (Specifically, on the letter a, it means it should be pronounced as "ay" instead of the usual "ah".)
A colon consists of two dots, one directly over the other, and it looks exactly like this :
There are two vowel sounds that can be considered a schwa in algebra (ahl-juh-bruh), the E and the second A.
Compare the distance to a known length. Measure. If you know the coordinates of the two dots in an orthogonal coordinate system, use Pythagoras' theorem to find the distance. Say point 1 has coordinate (Ax,By) and point 2 has coordinate (Cx,Dy) then the distance between 1 and 2 is the square root of ((C-A)2 + (D-B)2))
Yes. The original denominator and its conjugate will form the factors of a Difference of Two Squares (DOTS) and that will rationalise the denominator but only if the radicals are SQUARE roots.