Assume that a bird of mass 1.5 kg is held in a box at height 500m and this setup is placed on a weighing machine. Now, the bird starts to hover in the box  pushing the air downwards, and is at a height of around 450 m. If we measure the weight of the box, will we measure the bird's weight also. Consider air friction.  I believe that due to friction of air, the downward movement of the air may not touch the bottom of the box (the bird is hovering at around 450 m height) and is lost. Hence, we cannot measure the weight of bird.    Is this true?
Let thing of a bird standing still in a box on top of a weighing machine that shows a mass $m_0$. Now, imagine that the bird is flying, still in the same box and the same weighing machine shows a mass $m_1$. As the bird when flying, is applying a force towards the weighing machine, could we deduce that $m_0 = m_1$? I'm asking this question because saying that these masses are equal makes me as uncomfortable as saying that they are not equal and can't figure the right answer. So does $m_0 = m_1$ and why?
Export nodes from Drupal 4? Range of A and null space of the transpose of A So I'm complete stuck with something. I know it the following statements are true (or at least the seem to be from the results that I got from messing around with it a bit on MATLAB), but I don't understand why they are true or how to show so. Let $A$ be and $m$X$n$ matrix. Show that:  a) if $x \in N(A^TA)$ then $Ax$ is in both $R(A)$ and $N(A^T)$.   For this one I messed around with it with my own examples and I got $Ax=0$, therefore satisfing the statement, but I don't understand what's actually going on.   b) $N(A^TA)=N(A)$  again, makes sense when I see the results in MATLAB, but don't undestand why it works.  c) $A$ and $A^TA$ have the same rank  d) If $A$ has linearly independent columns, the $A^TA$ is nonsingular.  For the last two I have no idea on how to even start showing the relationship. I feel like I'm missing some crucial relationship between $A$ and $A^TA$, but I'm just not seeing it.   I would greatly appreciate any help of sugestions on how to show that these statements are true.   Thank you very much. Where can I send feature requests? Both for Ubuntu as a whole and individual (supported) apps? 3/4 circle with plus in it? If $a,b,c$ are positive real numbers, not all equal, prove that  $$\dfrac{bc}{b+c}+\dfrac{ca}{c+a}+\dfrac{ab}{a+b}&lt;\dfrac{a+b+c}{2}$$  Progress: $\frac{bc}{b+c}-\frac{b+c}{2}=$ How to rename a group of files with what looks like a Windows file path in their names I got a bunch of files with the filename messed up. All the file names have the same beginning which appear to be windows file directories. The problem is there are 700+ files and I really don't want go through and manually rename all of them. These are examples of the file names (Note: None of these have file directories):  G:some\really\long\file\path\then\the\name1.jpg G:some\really\long\file\path\then\the\name2.png G:some\really\long\file\path\then\the\filename.txt G:some\really\long\file\path\then\the\file_name.mov ...   The important take away is that each file has G:some\really\long\file\path\then\the\ before the file name that I would like.   So I would want the above files to look like:  name1.jpg name2.png filename.txt file_name.mov   I've tried the rename command and was not successful. I am still new with Linux and really am not sure on how to go about it or really what to google. Any help would be appreciated. Ubuntu 20.04 interface font too small after restart, even with high scaling factor So I was configuring VS code on my Notebook when suddenly I noticed that my interface font got really small on my desktop, terminal and files. I use Gnome Tweaks Tool to increase my scaling factor to 1,15 , but, even though it was active, the font stayed tiny. The solution I found was moving my scaling factor, which instantly fixed my font issue, however, every time I restart my Notebook the font gets tiny again and I have to repeat the process. I tried reseting my font configuration using this command, but had no success. gsettings reset org.gnome.desktop.interface text-scaling-factor  I also tried using the command dconf reset -f /  Finally, I tried using dconf-editor, but still had no success altering the font rendering DPI or changing the scaling factor. All of the steps I mentioned fixed my fonts temporarily, but the issue still persists when I restart my Notebook I am out of ideas and even considered getting a fresh Ubuntu install by now... My video card: NVIDIA GeForce GTX 1050 GPU What is the best way to add options to a select from a JavaScript object with jQuery? Will Windows 10 Technical Preview be upgradable to final release? Is there any information about if Windows 10 Technical Preview will then be upgradable to the final release ?  I'm asking that because I would like to use it on my primary PC (I'm aware of the risks but I accept them), in place of Windows 8.1 But I'd like to avoid to reinstall all after the release of the final version. How to set up RAID 1? Cannot update/get any packages. gedit not installed my problem is that my sources.list is out of date for some reason. I already found the fix in another port, but it doesn't work. It says to use gedit to edit sources.list and replace everything with the proper sources. Well, for some reason I don't have it installed (Ubuntu Server 14.04) and I can't install it or else I get the main problem again.  Failed to fetch http:// some ubuntu site Could not resolve hostname "us.archive.ubuntu.com"  Is there any other way to edit sources.list? Or do I need to do a re-install of the OS? Query to find GUID's "not in" null containing subquery returns no results Minecraft Survival Mode I am playing Minecraft on survival mode. I can break blocks like sand, dirt, and gravel and it will give me a block. When I try to break stone or iron or anything else, it didn't give me a block. What can I do so that I can get a block? I am on single player and my internet is fine. I tried deleting the app and then getting the app again but that didn't work. This is happening with all my worlds in survival mode. Is it possible to turn off radio without turning of wifi on Lenovo k900? I am currently having a look at the power consumption of a lenovo k900 phone and on the hardware side it seems Radio and Screen is using most of the power.  I am planning to use wifi but not the radio. Are they disconnected ? If so, can I use just the wifi, but no radio/telephony ? Are the settings or commands/intents to access these settings ?  Thanks! SF Story about human adapting to alien environment How to create a YouTube playlist from a list of links? I have very long lists of YouTube links/bookmarks. I want to create playlists for my YouTube channel with them. Is there any way to do it automatically without having to add each individual URL to a playlist? I have been getting this question lately from students and although I have a lot of information to offer, I have not found a source that I can point people to where they can read an update answer (I have found a lot of misinformation and obsolete information). So, some of the questions I have for package formats like snap, appimage, flatpak and others in this evolution of universal packaging systems are:   Who created the package format? What features does it offer? What features are unique to it? (That the others do not yet have) Who supports it? What Distributions use it? What focus does the package have? (For Desktop, Clouds, Mobile, etc..) Which are more actively developed? Were any of the Elves in Tolkien twins? Thinking about the idea of Elves having low numbers overall, got me to wondering: as far as Tolkien's writing, could elves ever have twins?  As a "yes" answer, I need an example of twins (any of JRRT work). They must be full on Elves, not half-Men. As a "no" answer, has to be an explicit statement in his work stating Elves ALWAYS had one child at a time. Anything else is a "maybe, we don't know". Borel set preserved by continuous map Let $f:\mathbb{R}^m\rightarrow\mathbb{R}^n$ be a continuous map. Show that if $A$ is a Borel subset of $\mathbb{R}^n$, then $f^{-1}(A)$ is a Borel subset of $\mathbb{R}^m$.   I know that for $A$ open subset of $\mathbb{R}^n$, then $f^{-1}(A)$ is open. Likewise for closed. A Borel subset is a countable unions/intersections of these sets, done repeatedly. From those facts, combined with $f^{-1}(A\cup B)=f^{-1}(A)\cup f^{-1}(B)$ and $f^{-1}(A\cap B)=f^{-1}(A)\cap f^{-1}(B)$, the statement should be intuitively true.  But to do it rigorously, I want to write $A$ as open and closed sets. But since the countable union/intersection can be done repeatedly, I don't know how I can write it that way. Adverb sentence query