Consider a 2-dimensional surface with (r1,a2) = (0,ø) (the usual spherical polar angles) and metric ds2 rdo2? sin20 dd2, where ro> 0 is a constant. you are given that the only non-zero christoffel symbols are гу — га 2 2 1 cot 0 cos 0 г. - sin 12 21 22 (a) prove that if a contravariant vector a' undergoes parallel transport around the circle -п/4 from ф %—o to ф%3d 2т аnd a' — 0, a? 3d 1 at ф 3 0, then at ф — 2т we have acos(2t) sin(27) 2 a (b) show that the components ri1, r22 of the ricci tensor are r11 1 r22 -sin20 find r, the ricci scalar

Acetic acid  /əˈsiːtɪk/, systematically named  ethanoic acid  /ˌɛθəˈnoʊɪk/, is a colourless liquid  organic compound  with the  chemical formula  ch3cooh (also written as ch3co2h or c2h4o2). when undiluted, it is sometimes called  glacial acetic acid.  vinegar  is no less than 4% acetic acid by volume, making acetic acid the main component of vinegar apart from water. acetic acid has a distinctive sour taste and pungent smell. in addition to household vinegar, it is mainly produced as a precursor to  polyvinyl acetate  and  cellulose acetate. it is classified as a  weak acid  since it only partially  dissociates  in solution, but concentrated acetic acid is corrosive and can attack the skin.acetic acidnamespreferred iupac nameacetic acidsystematic iupac nameethanoic acidother namesvinegar (when dilute); hydrogen acetate; methanecarboxylic acid[1][2]identifierscas number64-19-7  3d model (jsmol)interactive image3dmetb00009 reference506007chebichebi: 15366  chemblchembl539  chemspider171  drugbankdb03166  echa infocard100.000.528ec number200-580-7e numbere260  (preservatives)gmelin reference1380iuphar/bps1058keggd00010  meshacetic+acidpubchem  cid176rtecs numberaf1225000uniiq40q9n063p  un number2789inchiinchi=1s/c2h4o2/c1-2(3)4/h1h3,(h,3,4)  key:   qtbsbxvteameqo-uhfffaoysa-n  smilescc(o)=o