Cookies to prevent multiple submissions

I'm running a basic survey using the code below followed by a form:

<%
If Request.Form("submit") = "Submit" Then
 ' Ensure there is some content
 If Len(Trim(Request.Form("Q1")) & Trim(Request.Form("Q2")) & Trim(Request.Form("Q3")) & Trim(Request.Form("Q4")) & Trim(Request.Form("Q5")) & Trim(Request.Form("Q6"))) > 0 Then
  set cn=server.createobject("adodb.connection")
  strConnect = "DRIVER={Microsoft Access Driver (*.mdb)};DBQ=" & Server.MapPath("/dbase/poll/CapitalPunishment.mdb")
  cn.open(strConnect)
  Set rs = Server.CreateObject("ADODB.RecordSet")
  strSQL = "SELECT * FROM Results"
  rs.Open strSQL,cn,3,3
  rs.AddNew
  rs("Question1") = Request.Form("Q1")
  rs("Question2") = Request.Form("Q2")
  rs("Question3") = Request.Form("Q3")
  rs("Question4") = Request.Form("Q4")
  rs("Question5") = Request.Form("Q5")
  rs("Question6") = Request.Form("Q6")
  rs.Update
  rs.Close
  cn.Close
  Set cn = Nothing
  mode = "thankyou"
 End If
End If
%>

I'd like to be able to set a cookie upon 'submit' of the form which will be checked if the person returns to this page.  If they have the cookie (meaning they've submitted their response already) they should then see the 'thank you' version of the page rather than the form.  What is the easiest way to do this?

Thanks!

Thanks Blair - it certainly gave me enough of a clue to work it out.  Just so you know, this is how I ended up getting it to do what I wanted:

<%
IF Request.Cookies("cp_submitted")="yes" Then
mode = "thankyou"
End If
If Request.Form("submit") = "Submit" Then
 ' Ensure there is some content
 If Len(Trim(Request.Form("Q1")) & Trim(Request.Form("Q2")) & Trim(Request.Form("Q3")) & Trim(Request.Form("Q4")) & Trim(Request.Form("Q5")) & Trim(Request.Form("Q6"))) > 0 Then
  set cn=server.createobject("adodb.connection")
  strConnect = "DRIVER={Microsoft Access Driver (*.mdb)};DBQ=" & Server.MapPath("/dbase/poll/CapitalPunishment.mdb")
  cn.open(strConnect)
  Set rs = Server.CreateObject("ADODB.RecordSet")
  strSQL = "SELECT * FROM Results"
  rs.Open strSQL,cn,3,3
  rs.AddNew
  rs("Question1") = Request.Form("Q1")
  rs("Question2") = Request.Form("Q2")
  rs("Question3") = Request.Form("Q3")
  rs("Question4") = Request.Form("Q4")
  rs("Question5") = Request.Form("Q5")
  rs("Question6") = Request.Form("Q6")
  Response.Cookies("cp_submitted")="yes"
  rs.Update
  rs.Close
  cn.Close
  Set cn = Nothing
  mode = "thankyou"
 End If
End If
%>