Yoran

I never (really) finished Alduin's Wall, because Esbern was bugged (I used a cheat to finish it, but I did download the esbern fix for the 'truce' in High Hrothgar). Now I'm trying to finish the Paarthunax mission, and I have to meet up with Delphine and Esbern in the sky haven temple, but I can't get in.

There's no response when I activate the blood seal. I tried walking out and back it, but it doesn't work. How do I get into sky haven temple? Is there a cheat that opens the door?

I don't want to load a save from alduin's wall, because I've pretty much finished the entire game since then (some 30 hours of playtime will be lost in going back).

Can someone check if my answer is correct?

Let G be a group of order 66. Then, using Cauchy's theorem, there exists an element x of order 3 and an element y of order 11. Now, we want to show that x and y commute, because in that case

ord(xy)=ord(x)ord(y).

Consider <x> and <y>, which are subgroups of G. Note that <x> has order 3 and <y> has order 11, which means that every non-identity element in <x> has order 3, and every non-identity element of <y> has order 11. So, the intersection of the two subgroups (which is again a subgroup), contains only the identity element.

Using the Sylow theorems, I've shown that there is only one 11-Sylow and only one 3-Sylow in G, which means both are normal, and also equal to <y> and <x> respectively. So <x> and <y> are normal subgroups.

Now consider xyx^-1y^-1. Using the fact that <y> is a normal subgroup, xyx^-1 is in y, and so

(xyx^-1)y^-1 is in <y>.

However, yx^-1y^-1 is a conjugate of x^-1, which is again in <x>, so xyx^-1y^-1 is also in <x>.

Hence it is in both <x> and <y>. But this only contained e, which means that xyx^-1y^-1 = e and thus xy=yx.

Now because x and y commute, we have

ord(xy) = ord(x)ord(y) = 33. So xy is an element of order 33 in G.

Is this correct? If not, what did I do wrong? If it is correct, is there any faster way you can prove this?

Let n be a natural number. How many elements of order n are there in O2?

Here 02 is the orthogonal group, consisting of matrices A in the general linear group of dimension 2 (over R), such that A^t A = AA^t = I.

I imagine that 02 consist of matrices in the plane R^2 , which are either reflections or rotations. For n=1 we just have the identity matrix, I. So there is just 1 element of order 1 ( as usual in a group).

I'm kind of stuck at n=2... I reckon all the reflections have order 2, but there are an infinte amount of lines you could reflect in, so there are an infinite amount of elements of order 2 which are just reflections...

For n>2 can you say that these have to be rotations, i.e. rotations over 2pi/3, and that there a 2 for every n>2 (rotating in two directions)?

I'm terrible at matrix groups, for some reason. Can anyone help me out :D ?

Some days ago, I answered this question in mathematics (see URL at the bottom). To my surprise someone actually copied my answer word by word (he also copied the other guys' answer!). Now I put quite some effort in that answer so it's kinda lame someone would just copy it like that and pretend he/she came up with it him/herself. What can I do about this?

link: http://answers.yahoo.com/question/index;%E2%80%A6

You can clearly see there are two answers from 5 days ago, the longest of which is mine, and one that contains both answers word by word from just 1 day ago.

I have already reported the person (no result), and I can't message him/her because names are not displayed any more.

Some days ago, I answered this question in mathematics (see URL at the bottom). To my surprise someone actually copied my answer word by word (he also copied the other guys' answer!). Now I put quite some effort in that answer so it's kinda lame someone would just copy it like that and pretend he/she came up with it him/herself. What can I do about this?

link: http://answers.yahoo.com/question/index;_ylt=AhzZ2...

You can clearly see there are two answers from 5 days ago, the longest of which is mine, and one that contains both answers word by word from just 1 day ago.

Very often people will approach me and ask me what my grades are, with the sole purpose of me asking them what grades they've got. Needless to say their grades are really high (they wouldn't have asked me otherwise), and they're not in the least bit interested in what I've achieved. These are about the same types of people that boast on and on about how little they learn and 'still' manage to keep a 4.0 GPA.

So now I'm trying to think of good replies, preferrably ones that will confront them with how annoying and anti-social they're acting, hopefully shutting them up forever. I've actually tried to not ask them back what their grades are, but they tend to tell me anyways. Can you guys please help me?

P.S I know that I might come across as some jealous guy. Trust me, I'm not. I'm perfectly okay with my grades, I just can't stand these insecure people rubbing their grades in my face anymore.