I found this on  on Symmetry Magazine:     The size of an atom is governed by the average location of its electrons. Nuclei are around 100,000 times smaller than the atoms they’re housed in. If the nucleus were the size of a peanut, the atom would be about the size of a baseball stadium. If we lost all the dead space inside our atoms, we would each be able to fit into a particle of lead dust.   Could somebody show the math to come to this conclusion?  I don't know a lot about physics but I like to learn. My question aims to asses how much I can trust the analogy in the article: The particle physics of you.
Zero dimensional points do not take up space, so then wouldn't everything in the universe be literally empty? Or is there something that I'm missing?
I have to determine how many six-integer subsets of $\{1, 2, 3, \ldots, 20\}$ are possible if no two consecutive integers are in a set. Extra slash added to the chat room URLs in the side bar Disposing WPF User Controls What does a linear transformation do to a vector in $\mathbb{R}^2$ $\newcommand{\Reals}{\mathbb{R}}$Doing some linear algebra. This question has me intrigued. I imagine it causes the vector to rotates the $x$ axis. But I mean, is there more to it?  $$ T_{A(\theta)}: \Reals^2 \to \Reals^2,\qquad A(\theta) =  \left[\begin{array} {rr}\cos \theta &amp; -\sin \theta \\   \sin \theta &amp; \cos \theta \\ \end{array}\right]. $$ What, geometrically, does the linear transformation $T_{A(\theta)}$ do to a vector in $\Reals^2$? Why can "find" not be used in PowerShell? What does find.exe find objectionable about the parameters when it is used in a PowerShell console shell?  These commands work as expected in a cmd.exe shell:  PS C:\Windows\System32\WindowsPowerShell\v1.0&gt; find /i "System.Diagnostics.Process" *.ps1xml FIND: Parameter format not correct PS C:\Windows\System32\WindowsPowerShell\v1.0&gt; find /i "System.Diagnostics.Process" *.ps1xml FIND: Parameter format not correct PS C:\Windows\System32\WindowsPowerShell\v1.0&gt; C:\Windows\System32\find.exe /i "System.Diagnostics.Process" *.ps1xml FIND: Parameter format not correct PS C:\Windows\System32\WindowsPowerShell\v1.0&gt; C:\Windows\System32\find.exe /i "System.Diagnostics.Process" .\DotNetTypes.format.ps1xml FIND: Parameter format not correct Neural network - meaning of weights I've been wondering, what is the difference between seek and search? When should one be preferred over the other? Got a working screen via HDMI, but the DVI won't go past 1360x768 (a PackardBell Maestro monitor). Had no issues in Windows 7.  I've tried all the xrandr tricks, see the output below:   xrandr  Screen 0: minimum 8 x 8, current 3280 x 1080, maximum 16384 x 16384 VGA-0 disconnected (normal left inverted right x axis y axis) DVI-D-0 disconnected (normal left inverted right x axis y axis) HDMI-0 connected primary 1920x1080+1360+0 (normal left inverted right x axis y axis) 510mm x 287mm    1920x1080      60.0*+   59.9     50.0      1680x1050      60.0      1600x900       60.0      1440x900       59.9      1280x1024      75.0     60.0      1280x800       59.8      1280x720       60.0     59.9     50.0      1152x864       75.0      1024x768       75.0     70.1     60.0      800x600        75.0     72.2     60.3     56.2      720x576        50.0      720x480        59.9      640x480        75.0     72.8     59.9   DVI-D-1 connected 1360x768+0+0 (normal left inverted right x axis y axis) 0mm x 0mm    1024x768       60.0 +    1360x768       60.0*    59.8      1152x864       60.0      800x600        72.2     60.3     56.2      680x384        60.0     59.8      640x480        59.9      512x384        60.0      400x300        72.2      320x240        60.1     cvt 1920 1080 # 1920x1080 59.96 Hz (CVT 2.07M9) hsync: 67.16 kHz; pclk: 173.00 MHz Modeline "1920x1080_60.00"  173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsync  xrandr --newmode "test" 173.00  1920 2048 2248 2576  1080 1083 1088 1120 -hsync +vsync  xrandr --addmode DVI-D-1 test X Error of failed request:  BadMatch (invalid parameter attributes)   Major opcode of failed request:  140 (RANDR)   Minor opcode of failed request:  18 (RRAddOutputMode)   Serial number of failed request:  37   Current serial number in output stream:  38    I'm using the latest driver from Nvidia (binary, 352.63) because Nouveau would show a black screen on my second monitor.  I got stuck on manually finding/creating a xorg.conf file and adding some monitor hacks, can anyone help me? What is the title of a 80's (i believe?) movie where humans in the far future are going extinct, and are aquiring new humans by going back in time to todays world, kidnapping air travelers that are known to have died that day, from the flying passenger aircraft just before its crashing.  A key visual:    Inside a hangar, a time portal opened, and a tail of a (flying) passenger aircraft extruded into the hangar where a stairs provided access to the back door of the aircraft.  The kidnappers made sure the surviving passengers remain seated and would forget about the whole ordeal. Kidnapped humans got replaced by lookalike dummies, including things they had on them. They tried hard not to alter the timeline. Noun for "person with intermediate skill" I'm looking for the noun form of "person with intermediate skill". For example, in the context of a particular activity, "person with no skill" might be designated a novice, and "person with much skill" might be designated an expert. However I know of no such word in between these two extremes.   My only thought is amateur, which has a distinct meaning from describing level of skill, although skill level can often be inferred. I'm looking for a better solution.  EDIT: due to the attention this question has received, I'll try to offer some clarification in order to reduce repeat questions.   "Journeyman" would certainly not work. I am a software developer by profession. However the word I'm looking for should hopefully be profession-agnostic. I am trying to designate the skill level of the person that some learning material might be appropriate for. The word that I'm looking for follows the preposition "for".   For Beginners  For [word for intermediate-skilled person] For Experts  Sorry, but even after all the great answers, I'm still learning towards "amateur" even though it is technically incorrect. Also, the word should not be so esoteric that only people with English degrees know what it means. Keep the ideas coming! In Iron Man 3, we saw that Tony was able to control Mark 42 armor remotely.  Talking about the Hulkbuster armor used in Avengers: Age of Ultron, it was very dangerous because Hulk's unpredictable rage could rip it apart any time.  Why didn't Iron Man simply control the Hulkbuster armor remotely? Explain $\iint \mathrm dx\,\mathrm dy = \iint r \,\mathrm \,d\alpha\,\mathrm dr$ Yes, I know the topic has been discussed before. I know that Meta already has threads that complain about how flagging doesn't work. I wanted to give a practical example.  Today, a  came in to the  chat and asked the :  Hey guys, as soon as I embed javascript, all my html elements are gone. Even if the script is empty!? ...Can anyone help out? The example is really minimalistic &lt;script type='text/javascript' src=&quot;http://ajax.googleapis.com/ajax/libs/jquery/2.0.3/jquery.min.js&quot;/&gt; &lt;script type='text/javascript' src=&quot;script.js&quot;/&gt; These lines make everything vanish. script.js is empty! I use google chrome and the file is on localhost  Some context:  The JS room encourages people to come and ask questions that are too small/badly put for main. The room encourages people to just ask questions rather than ask to ask. In fact we even have a bot that prompts users to just ask if they have a question whenever they join. The above user has a good Q to A ratio having 1K rep in the main site and over 80 answers. The user has no negative context in the chat. No previous offenses or anything like that.  That message got 7 flags  Had a mod (ThiefMaster) not been present and invalidated those flags in time that user would have probably been suspended from the chat. This is bad, it sends the wrong message and it is very rude. Now, some other rooms don't allow people to just come and ask questions right away so maybe users from other rooms validated the flag. Maybe users thought he was being rude? I don't know. I do know that we don't want this sort of negative atmosphere in the JS room (and I'm sure other useful rooms such as PHP don't want it either), we have enough on our hands trying to maintain a community while helping people joining and handing with vamps/trolls. Possible solutions:  Drop spam/offensive flags altogether. Make spam/offensive flags room specific for big enough (tm) rooms. Give room owners just the ability to invalidate spam/offensive flags. I've got a domain that I apparently forgot to set a preferred domain for, so I just tried to do it. Webmaster Tools instead popped up a little box:     Part of the process of setting a preferred domain is to verify that you own http://www.example.com/. Please verify http://www.example.com/.   I'm running into some problems following these instructions:   As far as I can tell I already did verify sometime in the past. There's a TXT DNS record with the gibberish Google tells you to set for it that I couldn't have come up with myself. …and nothing is telling me this information is bad. So let's assume the site is somehow not actually verified. All  instructions start with "click the Manage Site button next to the site you want, and then click Verify this site." That button doesn't even exist on my screens. (It presumably goes away when you successfully verify?) Those instructions were all updated pretty recently, and the DNS one in particular just a couple weeks ago so it seems a bit unlikely they're inaccurate.   I am not using Apps, and won't be, so can't try out the verification .   Note that I also have another domain that I have not done any verification for which is showing the same behavior(no such button, being told to verify when it seems impossible etc.) so something appears to just be broken.  I already have a no-www process in place server-side, so we can skip that. I'm just trying to get the box checked off in GWT.  If I don't get any resolution, I'll eventually scrap the TXT record and see if the site gets un-verified(or whatever since it thinks it isn't), and see if I can just restart the process.  It's not urgent so I'm just trying to figure out if I've gone blind to something or what. Did the button move? Prove the compactness of a set B We have $A=\left\lbrace 2019,1010,\ldots,(n+2018)/n,\ldots \right\rbrace$ and $B=A \cup \left\lbrace 1 \right\rbrace$  How can I show directly (that is, not using the compactness criterion in $\mathbb{R}$) that every open cover $G$ of $B$ admits a finite subcover?  moreover, I know that $A$ is not compact and I am aware that I would need a single example to prove it, any hint on how to find an open cover of $A$ that does not contain a finite subcover?  My first thought was to choose the set of all neighborhoods with radius r centered around each point of A but apparently this is wrong and I do not understand why. Backtrack, Wi-Fi not working I've installed Backtrack 5R3 KDE, and I realized that my wireless is not working, but wired is working fine.  Here's the lshw output:     *-network         description: Ethernet interface         product: RTL8101E/RTL8102E PCI Express Fast Ethernet controller         vendor: Realtek Semiconductor Co., Ltd.         physical id: 0         bus info: pci@0000:02:00.0         logical name: eth0         version: 05         serial: 04:7d:7b:b7:46:f8         size: 100MB/s         capacity: 100MB/s         width: 64 bits         clock: 33MHz         capabilities: pm msi pciexpress msix vpd bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd autonegotiation         configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl_nic/rtl8105e-1.fw ip=192.168.2.2 latency=0 link=yes multicast=yes port=MII speed=100MB/s         resources: irq:42 ioport:2000(size=256) memory:f0404000-f0404fff memory:f0400000-f0403fff   lspci output:      00:00.0 Host bridge: Intel Corporation 2nd Generation Core Processor Family DRAM Controller (rev 09) 00:02.0 VGA compatible controller: Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller (rev 09) 00:14.0 USB Controller: Intel Corporation Panther Point USB xHCI Host Controller (rev 04) 00:16.0 Communication controller: Intel Corporation Panther Point MEI Controller #1 (rev 04) 00:1a.0 USB Controller: Intel Corporation Panther Point USB Enhanced Host Controller #2 (rev 04) 00:1b.0 Audio device: Intel Corporation Panther Point High Definition Audio Controller (rev 04) 00:1c.0 PCI bridge: Intel Corporation Panther Point PCI Express Root Port 1 (rev c4) 00:1c.1 PCI bridge: Intel Corporation Panther Point PCI Express Root Port 2 (rev c4) 00:1d.0 USB Controller: Intel Corporation Panther Point USB Enhanced Host Controller #1 (rev 04) 00:1f.0 ISA bridge: Intel Corporation Panther Point LPC Controller (rev 04) 00:1f.2 SATA controller: Intel Corporation Panther Point 6 port SATA AHCI Controller (rev 04) 00:1f.3 SMBus: Intel Corporation Panther Point SMBus Controller (rev 04) 02:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8101E/RTL8102E PCI Express Fast Ethernet controller (rev 05) I wanna create a new partition from the existing root partition.My root partition is about 250GB.I wanna create a new partition say 150 GB taking space from this root partition.Can anyone help me with the procedure on doing this?  output: fdisk -l  karthick@karthick:~$ sudo fdisk -l [sudo] password for karthick:   Disk /dev/sda: 250.0 GB, 250000000000 bytes 255 heads, 63 sectors/track, 30394 cylinders Units = cylinders of 16065 * 512 = 8225280 bytes Sector size (logical/physical): 512 bytes / 512 bytes I/O size (minimum/optimal): 512 bytes / 512 bytes Disk identifier: 0x28219744  Device Boot      Start         End      Blocks   Id  System /dev/sda1   *           1          61      487424   83  Linux Partition 1 does not end on cylinder boundary. /dev/sda2              61       30395   243650561    5  Extended /dev/sda5              61         124      498688   82  Linux swap / Solaris /dev/sda6             124         186      498688   82  Linux swap / Solaris /dev/sda7             186       30395   242651136   83  Linux I'm new in LaTex. I need to draw a graphic like the image and each rectangles of image must have the size shown in Figure. I drwan it by MS power point but I need to do by LaTex. Can you help me? Thank you in advance for your help and collaboration!  Thank you in advance for your help and collaboration! What are the functions that are their own inverse?  (thus functions where $ f(f(x)) = x $ for a large domain)  I always thought there were only 4:  $f(x) = x , f(x) = -x , f(x) = \frac {1}{x} $ and $ f(x) = \frac {-1}{x} $   Later I heard about a fifth one     $$f(x) = \ln\left(\frac {e^x+1}{e^x-1}\right) $$ (for $x &gt; 0$)  This made me wonder are there more? What are conditions that apply to all these functions to get more, etc. Redirect after user login