Good evening!  I want to create a bibliography for a thesis but I can't download the related Libreoffice tool because the necessary package is untrusted for my computer. Each time I try I get the following error message:  libreoffice-base libreoffice-base-drivers libreoffice-sdbc-firebird libreoffice-sdbc-hsqldb    Here is a pic of the situation:    Can you help me download it or find an alternative solution?
I tried installing VLC Player yesterday, and I got the Requires installation of untrusted packages error.  I searched for hours for a solution to this problem, and finally came upon a suggestion that said to change servers for downloading updates from.  I did this, and it gave me a 404 error when I clicked on "Check" in the Update Manager.  I tried switching my server back to the main one (and after that, several other ones), but I am now still getting a 404 error:   And the other error I get when downloading or updating:   Edit: Output of cat /etc/apt/sources.list:  deb-src http://us.archive.ubuntu.com/ubuntu/ precise main restricted #Added by software-properties  # See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to # newer versions of the distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise multiverse universe #Added by software-properties  ## Major bug fix updates produced after the final release of the ## distribution. deb http://us.archive.ubuntu.com/ubuntu/ precise-updates main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-updates restricted main multiverse universe #Added by software-properties  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu ## team. Also, please note that software in universe WILL NOT receive any ## review or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise universe deb http://us.archive.ubuntu.com/ubuntu/ precise-updates universe  ## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu  ## team, and may not be under a free licence. Please satisfy yourself as to  ## your rights to use the software. Also, please note that software in  ## multiverse WILL NOT receive any review or updates from the Ubuntu ## security team.  ## N.B. software from this repository may not have been tested as ## extensively as that contained in the main release, although it includes ## newer versions of some applications which may provide useful features. ## Also, please note that software in backports WILL NOT receive any review ## or updates from the Ubuntu security team. deb http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-backports main restricted universe multiverse #Added by software-properties  deb http://us.archive.ubuntu.com/ubuntu/ precise-security main restricted multiverse deb-src http://us.archive.ubuntu.com/ubuntu/ precise-security restricted main multiverse universe #Added by software-properties deb http://us.archive.ubuntu.com/ubuntu/ precise-security universe  ## Uncomment the following two lines to add software from Canonical's ## 'partner' repository. ## This software is not part of Ubuntu, but is offered by Canonical and the ## respective vendors as a service to Ubuntu users. deb http://archive.canonical.com/ubuntu precise partner deb-src http://archive.canonical.com/ubuntu precise partner  ## This software is not part of Ubuntu, but is offered by third-party ## developers who want to ship their latest software.
Physically what does warping (of space-time) mean? So there's general relativity and Einstein's field equations that tell us "mass(or equivalently energy) warps space-time, and the warping tells mass how to move", but I'm still having trouble understanding how space (a thing I conceive to be 'empty' or nothingness) can be 'warped'.  After researching books, on-line articles, and this stack exchange itself I can't seem to find any descriptions or discussions that don't immediately resort to jumping into GR and its mathematics to provide a more physical intuitive understanding of what it means to for space to be warped.  Is it space, this empty thing, that's getting warped. Or rather is it some field (Higgs field?) that exists around matter that's getting warped?  Although this question appears similar to  , it's asking if it's empty space that's being warped by matter or rather a field in space that's being warped (the Higgs Field?). The other question and all 10 answers addressing it do not address fields vs. empty space - What's really getting warped? Snap packages each have their own copy of dependencies. This means there are lots of packages in each snap, which would equate to large package sizes. Wouldn't this mean that snaps would be so much bigger than traditional debs? How can I make them smaller? I have limited space. How does passive perception work Total noob question, but the passive perception is confusing. I don't understand how to calculate it or use it, and I need help. I can't seem to get this hat on straight! I carefully positioned my hat to fit my head just right:     But it seems to be shifted to the left a few pixels elsewhere (same in Firefox and Chrome):   Stack Overfow   Skeptics   The top bar is also affected on some sites:   Stack Overfow   Meta SE   InfoSec   However, it is in the correct position in the top bar on some sites somehow:   Skeptics   Bricks   It's not a huge deal of course, it just bothers perfectionists like me. Find a recurrence relation for the number of ternary strings of length n that do not contain two consecutive 0s or two consecutive 1s. Is there a way to set initial state with rigid bodies? Let's say I set up a Rigid Body simulation in Blender (not in GE), and then run the simulation for a number of frames. Is there a way to tell Blender to use the current state and position as the initial state? So that when I go back to frame 1, the rigid bodies stay in the same place they did in frame X.  For instance, if I want a pile of bricks, I first place the bricks in the air and then let them drop down on the ground, coming to rest. When they have come to rest, I want to use that position as the starting position. Complex Exponent of Complex Numbers How does one find the algebraic solution of a Complex number raised to the power of another Complex number?  Here is the work I have done so far, if there are any mistakes please inform me.  A real number with a Complex Exponent: $$A \in \Bbb R, \space z \in \Bbb C,\space z = x + iy$$ $$A^z = A^{x+iy} = A^xA^{iy}$$ $$\implies e^{iy\ln A} = A^{iy}$$ $$\exp(iy\ln A) = \cos (y\ln A)+i\sin(y\ln A)$$ $$A^z = A^x[\cos (y\ln A)+i\sin(y\ln A)]$$  A Complex number with a Complex Exponent: [Using previous variables] $$C \in \Bbb C,\space C = a +bi\space|\space re^{i\theta}, \theta =\arg C$$ $$C^z = (a+ib)^z$$ [After previous mistake the following notes are inaccurate] $$C^z = a^x[\cos (y\ln a)+i\sin(y\ln a)] + ib^xib^{iy}$$  And this is as far as I could go as the expansion of $ib^xib^{iy}$ is being problematic. Could I have some help with this expansion? What's an intuitive way to think about the determinant? In my linear algebra class, we just talked about determinants. So far I’ve been understanding the material okay, but now I’m very confused. I get that when the determinant is zero, the matrix doesn’t have an inverse. I can find the determinant of a $2\times 2$ matrix by the formula. Our teacher showed us how to compute the determinant of an $n \times n$ matrix by breaking it up into the determinants of smaller matrices. Apparently there is a way by summing over a bunch of permutations. But the notation is really hard for me and I don’t really know what’s going on with them anymore. Can someone help me figure out what a determinant is, intuitively, and how all those definitions of it are related? A student prepares for an exam by studying a list of 12 problems. She can solve 9 of them. For the exam, the instructor selects 7 problems at random from the 12 on the list given to the students. What is the probability that the student can solve 5 of the 7 problems on the exam?  I am really confused by this problem. My first initial thought was to do:  (5 chose 7)(7 chose 0)/ (12 chose 7)  I am not 100% sure about this though. Limit- almost finished, however hint needed. Prove the summation:  $$\sum_{i=1}^n i! \cdot i = (n+1)! - 1$$ using induction.   base case:  $n=1$: \begin{align*} \sum_{i=1}^1 i! \cdot i &amp;= (1+1)! - 1 \\ 1 &amp;= 2 - 1 \\ 1 &amp;= 1 \end{align*}   This is a question from my test review packet, currently have the base case completed and I am a bit lost on where to go from there. Any help/hints are appreciated. For some reason my iMac keeps turning off around 5 to 10 minutes into boot.  Also just recently it turns on but has shaded lines going down the screen. I have not installed any weird programs and i have not used it in around 3 months.   Any ideas on what the issue is, i don't have any other information about the issue besides whats happening when i use it.  The image i'm showing you was found on google but this looks exactly like mine does.  The model of my imac is the late 2011 model. Weird $3^n$ in an identity to be combinatorially proved Do the *Result objects in Database have a common ancestor? I'm doing some polymorphic programming, and I decided that I wanted to be able to gracefully handle partial saves using SaveResult without blocking the user experience. The code looks roughly like this:  static void logDmlErrors(SObject[] src, SObject[] dest, SaveResult[] results, String message) {     // Transform results into Chatter error messages, send them to admins }   I then went about writing the utility methods that would use this function:  public static void insertRecords(SObject[] src, SObject[] dest, String message) {     logDmlErrors(src, dest, Database.insert(dest, false), message); }   Everything went well, until I came across the delete and undelete methods, which instead use DeleteResult and UndeleteResult. Both of those two classes contain the exact same methods as SaveResult, and yet don't appear to inherit from a common ancestor. This means that I can't just cast to a super-type to get to this information.  Thankfully, Summer 16 apparently introduced support for serializing (and deserializing) these classes as JSON, so I do have a fairly expensive (but accurate) workaround if I want proper polymorphic behavior, but I thought I'd throw it out there and see if someone has an alternative solution to this problem. 8.00GB RAM (3.22GB usable) in Windows 7 x64 I have set up Windows 7 Ultimate 64-bit on my PC. I have 8GB RAM and my BIOS states the correct amount (8192MB), but Windows (System Manager) says I have 8.00GB (3.22GB usable). give me a solution. I'm tried this: Run &gt; MSCONFIG, open the Boot tab &gt; click Advanced Options &gt; make sure that Maximum Memory but this wasn't helpful. My Motherboard Details: CPU Type : DualCore Intel Pentium, 3000 MHz (15 x 200) Motherboard Name : Foxconn G41MXE Motherboard Chipset : Intel Eaglelake G41 System Memory : 3296 MB (DDR3-1333 DDR3 SDRAM) DIMM1: Kingston : 4 GB DDR3-1333 DDR3 DIMM3: Kingston : 4 GB DDR3-1333 DDR3 My BIOS Details: BIOS Type : AMI (03/21/11) Vendor : American Megatrends Inc. Version : 080015 Capabilities : Flash BIOS, Shadow BIOS, Selectable Boot, EDD, BBS System Properties :  Bios File :  What about Bios Update? Can independent variables with low correlation with dependent variable be significant predictors? I have eight independent variables and one dependent.  I have run a correlation matrix, and 5 of them have a low correlation with the DV.  I have then run a stepwise multiple regression to see whether any/all of the IVs can predict the DV.  The regression showed that only two IVs can predict the DV (can only account for about 20% of the variance though), and SPSS removed the rest from the model.  My supervisor reckons that I have not run the regression correctly, as due to the strength of the correlations, I should have found more predictors in the regression model. But the correlations were tiny, so my question is: if IVs and the DV hardly correlate, can IVs still be good predictors of the DV? Alpha and Omega limit sets (dynamical systems) What are all the possible $α$- and $ω$-limit sets of points for the linear system of equations $x'=Ax$ given by the following matrices $A$:  I guess I don't really know how to get started, Could I have some guidance? So I was told to calculate the eigenvalues (fine) and eigenvectors (I kind of forgot how to do that...)  I know that the $ω$-limit sets of points are the set of points that the system of equation approach as time goes to infinity, and the $α$-limit sets of points are the points approached as t goes to negative infinity.   $    A=   \left[ {\begin{array}{cc}    -4 &amp; -2 \\    3 &amp; 11 \\   \end{array} } \right] $   $λ_1=-10$ $λ_2=-5$  Since both eigenvalue are negative, this is a stable node, and the $ω$-limit set=0.  for $λ_1=-10$:  eigenvector $    =   \left[ {\begin{array}{cc}   1 \\    3 \\   \end{array} } \right] $  for $λ_2=-5$:  eigenvector $    =   \left[ {\begin{array}{cc}   2 \\    1 \\   \end{array} } \right] $   $    A=   \left[ {\begin{array}{cc}    1 &amp; 1 \\    3 &amp; 1 \\   \end{array} } \right] $   $λ_1=4$ $λ_2=-2$  Since one eigenvalue is positive and one is negative, it is not stable, so I can't use the same reasoning that I used above to find the $ω$-limit set... so I am not sure how to continue  for $λ_1=4$:  eigenvector $    =   \left[ {\begin{array}{cc}   1 \\    1 \\   \end{array} } \right] $  for $λ_2=-2$:  eigenvector $    =   \left[ {\begin{array}{cc}   -1 \\    1 \\   \end{array} } \right] $   $    A=   \left[ {\begin{array}{cc}    4 &amp; 5 \\    -5 &amp; -2 \\   \end{array} } \right] $   $λ_1=1+4i$ $λ_2=1-4i$  for $λ_1=1+4i$:  eigenvector $    =   \left[ {\begin{array}{cc}   -3/5-(4i)/5 \\    1 \\   \end{array} } \right] $  for $λ_1=1-4i$:  eigenvector $    =   \left[ {\begin{array}{cc}   -3/5+(4i)/5 \\    1 \\   \end{array} } \right]$ Does herd behavior influence the SO sites? Are you influenced by existing votes? That is, if a question or answer has a large number of up votes, are you more likely to vote it up (and similar for down)?  The reason I'm putting this question is this: on these sites we see how other people vote before we do. This almost certainly influences us (see resources, below) - just as we can be influenced by our  (people often naturally pick the busy one).  This trend may also be further influenced by rep - do we give more weight to the answer of someone with 10K rep than someone with 10 - even if they both have e.g. zero votes?  And if this does happen, is it even a problem?  I'm not looking here for solutions - right now I'm just curious as to whether this is something you recognise.  Clarification edit: I'm referring to voting here. Example: if you see a question or answer with 20 plus votes, are you more likely to vote it up than if it has no votes, or a negative number vote?  Bounty: I've been so impressed at the quality of answers and comments here that I'm offering a small bounty to encourage more great responses and discussion.  Wrapped up: Bounty awarded to the answer that received the most votes. In light of the question, it only seemed appropriate...  Resources: Why doesn't the Moon fall onto the Earth? What is the remainder of $\,3^{3^{3^{\:\!\phantom{}^{.^{.^.}}}}}\!\!\!$ divided by $46$?  The level of powers is $2020$.  First there is no parenthesis so it means 3 power of 3 which is also power 3 and so on 2020 times  Second I think that we can use Fermat's Little Theorem but I don't know how, and maybe there is a better way.